%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT393-1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:45:35 AM UTC 2026
% Result : Unsatisfiable 15.70s 2.50s
% Output : CNFRefutation 30.73s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
f(x0,f(f(x1,x2),f(x1,x2))) != f(x1,f(f(x0,x2),f(x0,x2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
neg(A) = f(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_003) ).
cnf(c3,plain,
neg(f(x1,x2)) = f(f(x1,x2),f(x1,x2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
f(f(x1,x2),f(x1,x2)) = neg(f(x1,x2)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
f(x0,f(f(x1,x2),f(x1,x2))) = f(x0,neg(f(x1,x2))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
f(neg(X2),neg(X)) = f(neg(X2),f(X,X)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
f(neg(X2),f(X,X)) = f(f(X2,X2),f(X,X)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
or(A2,B) = f(f(A2,A2),f(B,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_001) ).
cnf(c11,plain,
or(X2,X) = f(f(X2,X2),f(X,X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
f(f(X2,X2),f(X,X)) = or(X2,X),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
f(neg(X2),f(X,X)) = or(X2,X),
inference(transitivity,[status(thm)],[c9,c12]) ).
cnf(c14,plain,
f(neg(X2),neg(X)) = or(X2,X),
inference(transitivity,[status(thm)],[c7,c13]) ).
cnf(c15,plain,
f(neg(X),neg(X)) = or(X,X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
or(X,X) = f(neg(X),neg(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
neg(neg(X)) = f(neg(X),neg(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
f(neg(X),neg(X)) = neg(neg(X)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
or(X,X) = neg(neg(X)),
inference(transitivity,[status(thm)],[c16,c18]) ).
cnf(c20,plain,
neg(neg(X)) = or(X,X),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
f(neg(X),neg(X)) = or(X,X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c22,plain,
or(X,X) = f(neg(X),neg(X)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c24,plain,
f(neg(X),neg(X)) = f(f(X,X),neg(X)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
f(neg(X),X) = f(f(X,X),X),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
f(X,f(neg(X2),X2)) = f(X,f(f(X2,X2),X2)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
f(f(X,f(neg(X2),X2)),X3) = f(f(X,f(f(X2,X2),X2)),X3),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
f(X2,f(f(X2,f(neg(X3),X3)),X)) = f(X2,f(f(X2,f(f(X3,X3),X3)),X)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
f(f(f(f(X3,X2),f(X2,X)),X4),f(X2,f(f(X2,f(neg(X3),X3)),X))) = f(f(f(f(X3,X2),f(X2,X)),X4),f(X2,f(f(X2,f(f(X3,X3),X3)),X))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,axiom,
f(f(f(f(A2,B2),f(B2,C)),D),f(B2,f(f(B2,f(f(A2,A2),A2)),C))) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos) ).
cnf(c32,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))) = X3,
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(neg(X4),X4)),X2))) = X3,
inference(transitivity,[status(thm)],[c30,c32]) ).
cnf(c34,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(neg(X2),X2)),X))) = X3,
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(neg(X2),X2)),X))),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
f(X3,X3) = f(f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(neg(X2),X2)),X))),X3),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
f(f(X3,X3),neg(X3)) = f(f(f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(neg(X2),X2)),X))),X3),neg(X3)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
f(f(f(f(X4,X3),f(X3,X2)),f(and(X,f(X4,X3)),f(X,f(X4,X3)))),f(X3,f(f(X3,f(neg(X4),X4)),X2))) = X3,
inference(substitution,[status(thm)],[c33]) ).
cnf(c39,plain,
X3 = f(f(f(f(X4,X3),f(X3,X2)),f(and(X,f(X4,X3)),f(X,f(X4,X3)))),f(X3,f(f(X3,f(neg(X4),X4)),X2))),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
f(f(f(X4,X3),f(X3,X2)),X3) = f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X4,X3),f(X3,X2)),f(and(X,f(X4,X3)),f(X,f(X4,X3)))),f(X3,f(f(X3,f(neg(X4),X4)),X2)))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X3,X2)),X3)) = f(f(X4,X3),f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X4,X3),f(X3,X2)),f(and(X,f(X4,X3)),f(X,f(X4,X3)))),f(X3,f(f(X3,f(neg(X4),X4)),X2))))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
neg(f(X2,X)) = f(f(X2,X),f(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c43,axiom,
and(A2,B2) = f(f(A2,B2),f(A2,B2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_002) ).
cnf(c44,plain,
and(X2,X) = f(f(X2,X),f(X2,X)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
f(f(X2,X),f(X2,X)) = and(X2,X),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
neg(f(X2,X)) = and(X2,X),
inference(transitivity,[status(thm)],[c42,c45]) ).
cnf(c47,plain,
neg(f(X,X2)) = and(X,X2),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
and(X,X2) = neg(f(X,X2)),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
f(and(X,X2),f(X,X2)) = f(neg(f(X,X2)),f(X,X2)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
f(f(X3,X2),f(and(X,X3),f(X,X3))) = f(f(X3,X2),f(neg(f(X,X3)),f(X,X3))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
f(f(f(X4,X3),f(and(X2,X4),f(X2,X4))),X) = f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
f(f(X4,X3),f(f(f(X4,X3),f(and(X2,X4),f(X2,X4))),X)) = f(f(X4,X3),f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
f(X4,f(f(X4,X3),f(f(f(X4,X3),f(and(X2,X4),f(X2,X4))),X))) = f(X4,f(f(X4,X3),f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(X4,f(neg(X2),X2)),X3))) = X4,
inference(substitution,[status(thm)],[c33]) ).
cnf(c55,plain,
X4 = f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(X4,f(neg(X2),X2)),X3))),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
f(X4,f(f(X4,X3),f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X))) = f(f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(X4,f(neg(X2),X2)),X3))),f(f(X4,X3),f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
f(f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(X4,f(neg(X2),X2)),X3))),f(f(X4,X3),f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X))) = f(X4,X3),
inference(substitution,[status(thm)],[c33]) ).
cnf(c58,plain,
f(X4,f(f(X4,X3),f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X))) = f(X4,X3),
inference(transitivity,[status(thm)],[c56,c57]) ).
cnf(c59,plain,
f(X4,f(f(X4,X3),f(f(f(X4,X3),f(and(X2,X4),f(X2,X4))),X))) = f(X4,X3),
inference(transitivity,[status(thm)],[c53,c58]) ).
cnf(c60,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X4,X3),f(X3,X2)),f(and(X,f(X4,X3)),f(X,f(X4,X3)))),f(X3,f(f(X3,f(neg(X4),X4)),X2))))) = f(f(X4,X3),f(X3,X2)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
f(f(X3,X2),f(f(f(X3,X2),f(X2,X)),X2)) = f(f(X3,X2),f(X2,X)),
inference(transitivity,[status(thm)],[c41,c60]) ).
cnf(c62,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))) = f(f(f(f(X3,X2),f(X2,X)),X2),f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),X2)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))) = X2,
inference(substitution,[status(thm)],[c33]) ).
cnf(c65,plain,
f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),X2) = f(X2,X2),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,X2)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c68,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),neg(X2)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),neg(X2)),
inference(transitivity,[status(thm)],[c66,c69]) ).
cnf(c71,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))) = f(f(f(f(X3,X2),f(X2,X)),X2),neg(X2)),
inference(transitivity,[status(thm)],[c63,c70]) ).
cnf(c72,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),neg(X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))) = X2,
inference(substitution,[status(thm)],[c33]) ).
cnf(c74,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),neg(X2)) = X2,
inference(transitivity,[status(thm)],[c72,c73]) ).
cnf(c75,plain,
f(f(f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(neg(X2),X2)),X))),X3),neg(X3)) = X3,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
f(f(X,X),neg(X)) = X,
inference(transitivity,[status(thm)],[c37,c75]) ).
cnf(c77,plain,
f(neg(X),neg(X)) = X,
inference(transitivity,[status(thm)],[c24,c76]) ).
cnf(c78,plain,
or(X,X) = X,
inference(transitivity,[status(thm)],[c22,c77]) ).
cnf(c79,plain,
neg(neg(X)) = X,
inference(transitivity,[status(thm)],[c20,c78]) ).
cnf(c80,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
f(X2,X) = f(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c83,plain,
f(X2,neg(X)) = f(neg(neg(X2)),neg(X)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
f(neg(neg(X2)),neg(X)) = or(neg(X2),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c85,plain,
f(X2,neg(X)) = or(neg(X2),X),
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
f(X2,neg(neg(X))) = or(neg(X2),neg(X)),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
f(X2,X) = or(neg(X2),neg(X)),
inference(transitivity,[status(thm)],[c81,c86]) ).
cnf(c88,plain,
f(x1,x2) = or(neg(x1),neg(x2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
neg(f(x1,x2)) = neg(or(neg(x1),neg(x2))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
f(x0,neg(f(x1,x2))) = f(x0,neg(or(neg(x1),neg(x2)))),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
f(x0,neg(or(neg(x1),neg(x2)))) = or(neg(x0),or(neg(x1),neg(x2))),
inference(substitution,[status(thm)],[c85]) ).
cnf(c92,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c93,plain,
or(X2,X) = or(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
and(or(X2,X),X) = and(or(neg(neg(X2)),X),X),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c96,plain,
and(or(neg(X2),X),X) = and(or(neg(X2),X),neg(neg(X))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c98,plain,
or(neg(X2),X) = or(neg(X2),neg(neg(X))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
and(or(neg(X2),X),neg(neg(X))) = and(or(neg(X2),neg(neg(X))),neg(neg(X))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
or(neg(X2),neg(X)) = f(X2,X),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c101,plain,
and(or(neg(X2),neg(X)),neg(X)) = and(f(X2,X),neg(X)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c103,plain,
neg(and(X2,X)) = neg(neg(f(X2,X))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
neg(neg(f(X2,X))) = f(X2,X),
inference(substitution,[status(thm)],[c79]) ).
cnf(c105,plain,
neg(and(X2,X)) = f(X2,X),
inference(transitivity,[status(thm)],[c103,c104]) ).
cnf(c106,plain,
f(X2,X) = neg(and(X2,X)),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
and(f(X2,X),neg(X)) = and(neg(and(X2,X)),neg(X)),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
or(X2,X) = f(neg(X2),neg(X)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c109,plain,
neg(or(X2,X)) = neg(f(neg(X2),neg(X))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
neg(f(neg(X2),neg(X))) = and(neg(X2),neg(X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c111,plain,
neg(or(X2,X)) = and(neg(X2),neg(X)),
inference(transitivity,[status(thm)],[c109,c110]) ).
cnf(c112,plain,
neg(or(and(X2,X),X)) = and(neg(and(X2,X)),neg(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c113,plain,
and(neg(and(X2,X)),neg(X)) = neg(or(and(X2,X),X)),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c115,plain,
or(and(X,X2),X2) = or(and(X,X2),neg(neg(X2))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
and(X2,or(and(X,X2),X2)) = and(X2,or(and(X,X2),neg(neg(X2)))),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
neg(f(X,X)) = and(X,X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c118,plain,
and(X,X) = neg(f(X,X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c120,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
neg(f(X,X)) = neg(neg(X)),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
and(X,X) = neg(neg(X)),
inference(transitivity,[status(thm)],[c118,c121]) ).
cnf(c123,plain,
neg(neg(X)) = and(X,X),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
or(and(X,X2),neg(neg(X2))) = or(and(X,X2),and(X2,X2)),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
and(X2,or(and(X,X2),neg(neg(X2)))) = and(X2,or(and(X,X2),and(X2,X2))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c127,plain,
f(neg(X2),X) = f(neg(X2),neg(neg(X))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
f(neg(X2),neg(neg(X))) = or(X2,neg(X)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c129,plain,
f(neg(X2),X) = or(X2,neg(X)),
inference(transitivity,[status(thm)],[c127,c128]) ).
cnf(c130,plain,
f(neg(X),X) = or(X,neg(X)),
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
or(X,neg(X)) = f(neg(X),X),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
and(X,or(X2,neg(X2))) = and(X,f(neg(X2),X2)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
or(and(X2,or(X3,neg(X3))),neg(X)) = or(and(X2,f(neg(X3),X3)),neg(X)),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
and(X2,or(and(X2,or(X3,neg(X3))),neg(X))) = and(X2,or(and(X2,f(neg(X3),X3)),neg(X))),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
or(or(and(X3,X2),and(X2,X)),and(X2,or(and(X2,or(X3,neg(X3))),neg(X)))) = or(or(and(X3,X2),and(X2,X)),and(X2,or(and(X2,f(neg(X3),X3)),neg(X)))),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
neg(f(X,f(neg(X2),X2))) = and(X,f(neg(X2),X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c137,plain,
and(X,f(neg(X2),X2)) = neg(f(X,f(neg(X2),X2))),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
or(and(X2,f(neg(X3),X3)),neg(X)) = or(neg(f(X2,f(neg(X3),X3))),neg(X)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
and(X2,or(and(X2,f(neg(X3),X3)),neg(X))) = and(X2,or(neg(f(X2,f(neg(X3),X3))),neg(X))),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
or(or(and(X3,X2),and(X2,X)),and(X2,or(and(X2,f(neg(X3),X3)),neg(X)))) = or(or(and(X3,X2),and(X2,X)),and(X2,or(neg(f(X2,f(neg(X3),X3))),neg(X)))),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
f(f(X2,f(neg(X3),X3)),X) = or(neg(f(X2,f(neg(X3),X3))),neg(X)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c142,plain,
or(neg(f(X2,f(neg(X3),X3))),neg(X)) = f(f(X2,f(neg(X3),X3)),X),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
and(X2,or(neg(f(X2,f(neg(X3),X3))),neg(X))) = and(X2,f(f(X2,f(neg(X3),X3)),X)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
or(or(and(X3,X2),and(X2,X)),and(X2,or(neg(f(X2,f(neg(X3),X3))),neg(X)))) = or(or(and(X3,X2),and(X2,X)),and(X2,f(f(X2,f(neg(X3),X3)),X))),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
neg(f(X2,f(f(X2,f(neg(X3),X3)),X))) = and(X2,f(f(X2,f(neg(X3),X3)),X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c146,plain,
and(X2,f(f(X2,f(neg(X3),X3)),X)) = neg(f(X2,f(f(X2,f(neg(X3),X3)),X))),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
or(or(and(X3,X2),and(X2,X)),and(X2,f(f(X2,f(neg(X3),X3)),X))) = or(or(and(X3,X2),and(X2,X)),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c149,plain,
or(and(X3,X2),and(X2,X)) = or(and(X3,X2),neg(f(X2,X))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
or(or(and(X3,X2),and(X2,X)),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))) = or(or(and(X3,X2),neg(f(X2,X))),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c152,plain,
or(and(X3,X2),neg(f(X2,X))) = or(neg(f(X3,X2)),neg(f(X2,X))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
or(or(and(X3,X2),neg(f(X2,X))),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))) = or(or(neg(f(X3,X2)),neg(f(X2,X))),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
f(f(X3,X2),f(X2,X)) = or(neg(f(X3,X2)),neg(f(X2,X))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c155,plain,
or(neg(f(X3,X2)),neg(f(X2,X))) = f(f(X3,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
or(or(neg(f(X3,X2)),neg(f(X2,X))),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))) = or(f(f(X3,X2),f(X2,X)),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
f(neg(f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(neg(X3),X3)),X))) = or(f(f(X3,X2),f(X2,X)),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c158,plain,
or(f(f(X3,X2),f(X2,X)),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))) = f(neg(f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(neg(X3),X3)),X))),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
neg(f(f(X3,X2),f(X2,X))) = f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c160,plain,
f(neg(f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(neg(X3),X3)),X))) = f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(neg(X3),X3)),X))),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(neg(X3),X3)),X))) = X2,
inference(substitution,[status(thm)],[c33]) ).
cnf(c162,plain,
f(neg(f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(neg(X3),X3)),X))) = X2,
inference(transitivity,[status(thm)],[c160,c161]) ).
cnf(c163,plain,
or(f(f(X3,X2),f(X2,X)),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))) = X2,
inference(transitivity,[status(thm)],[c158,c162]) ).
cnf(c164,plain,
or(or(neg(f(X3,X2)),neg(f(X2,X))),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))) = X2,
inference(transitivity,[status(thm)],[c156,c163]) ).
cnf(c165,plain,
or(or(and(X3,X2),neg(f(X2,X))),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))) = X2,
inference(transitivity,[status(thm)],[c153,c164]) ).
cnf(c166,plain,
or(or(and(X3,X2),and(X2,X)),neg(f(X2,f(f(X2,f(neg(X3),X3)),X)))) = X2,
inference(transitivity,[status(thm)],[c150,c165]) ).
cnf(c167,plain,
or(or(and(X3,X2),and(X2,X)),and(X2,f(f(X2,f(neg(X3),X3)),X))) = X2,
inference(transitivity,[status(thm)],[c147,c166]) ).
cnf(c168,plain,
or(or(and(X3,X2),and(X2,X)),and(X2,or(neg(f(X2,f(neg(X3),X3))),neg(X)))) = X2,
inference(transitivity,[status(thm)],[c144,c167]) ).
cnf(c169,plain,
or(or(and(X3,X2),and(X2,X)),and(X2,or(and(X2,f(neg(X3),X3)),neg(X)))) = X2,
inference(transitivity,[status(thm)],[c140,c168]) ).
cnf(c170,plain,
or(or(and(X3,X2),and(X2,X)),and(X2,or(and(X2,or(X3,neg(X3))),neg(X)))) = X2,
inference(transitivity,[status(thm)],[c135,c169]) ).
cnf(c171,plain,
or(or(and(X2,X3),and(X3,X)),and(X3,or(and(X3,or(X2,neg(X2))),neg(X)))) = X3,
inference(substitution,[status(thm)],[c170]) ).
cnf(c172,plain,
X3 = or(or(and(X2,X3),and(X3,X)),and(X3,or(and(X3,or(X2,neg(X2))),neg(X)))),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
and(X3,or(and(X2,X3),and(X3,X))) = and(or(or(and(X2,X3),and(X3,X)),and(X3,or(and(X3,or(X2,neg(X2))),neg(X)))),or(and(X2,X3),and(X3,X))),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c175,plain,
or(X2,and(or(X2,X),and(neg(X2),neg(X)))) = or(neg(neg(X2)),and(or(X2,X),and(neg(X2),neg(X)))),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
and(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X))))) = and(or(X2,X),or(neg(neg(X2)),and(or(X2,X),and(neg(X2),neg(X))))),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c178,plain,
or(X2,X) = or(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
and(or(X2,X),and(neg(X2),neg(X))) = and(or(neg(neg(X2)),X),and(neg(X2),neg(X))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
or(neg(neg(X2)),and(or(X2,X),and(neg(X2),neg(X)))) = or(neg(neg(X2)),and(or(neg(neg(X2)),X),and(neg(X2),neg(X)))),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
and(or(X2,X),or(neg(neg(X2)),and(or(X2,X),and(neg(X2),neg(X))))) = and(or(X2,X),or(neg(neg(X2)),and(or(neg(neg(X2)),X),and(neg(X2),neg(X))))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c183,plain,
or(X2,X) = or(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
and(or(X2,X),or(neg(neg(X2)),and(or(neg(neg(X2)),X),and(neg(X2),neg(X))))) = and(or(neg(neg(X2)),X),or(neg(neg(X2)),and(or(neg(neg(X2)),X),and(neg(X2),neg(X))))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c186,plain,
and(X2,neg(X)) = and(neg(neg(X2)),neg(X)),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
and(or(neg(X2),X),and(X2,neg(X))) = and(or(neg(X2),X),and(neg(neg(X2)),neg(X))),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
or(neg(X2),and(or(neg(X2),X),and(X2,neg(X)))) = or(neg(X2),and(or(neg(X2),X),and(neg(neg(X2)),neg(X)))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
and(or(neg(X2),X),or(neg(X2),and(or(neg(X2),X),and(X2,neg(X))))) = and(or(neg(X2),X),or(neg(X2),and(or(neg(X2),X),and(neg(neg(X2)),neg(X))))),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
neg(or(neg(X2),X)) = and(neg(neg(X2)),neg(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c191,plain,
and(neg(neg(X2)),neg(X)) = neg(or(neg(X2),X)),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
and(or(neg(X2),X),and(neg(neg(X2)),neg(X))) = and(or(neg(X2),X),neg(or(neg(X2),X))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
or(neg(X2),and(or(neg(X2),X),and(neg(neg(X2)),neg(X)))) = or(neg(X2),and(or(neg(X2),X),neg(or(neg(X2),X)))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
and(or(neg(X2),X),or(neg(X2),and(or(neg(X2),X),and(neg(neg(X2)),neg(X))))) = and(or(neg(X2),X),or(neg(X2),and(or(neg(X2),X),neg(or(neg(X2),X))))),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
neg(f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))) = and(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c196,plain,
and(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = neg(f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))),
inference(symmetry,[status(thm)],[c195]) ).
cnf(c197,plain,
f(neg(neg(X2)),neg(X)) = or(neg(X2),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c198,plain,
or(neg(X2),X) = f(neg(neg(X2)),neg(X)),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = f(f(neg(neg(X2)),neg(X)),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
neg(neg(X)) = and(X,X),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c201,plain,
f(neg(neg(X2)),X) = f(and(X2,X2),X),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = f(f(and(X2,X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
neg(f(X,X)) = and(X,X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c204,plain,
and(X,X) = neg(f(X,X)),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
f(and(X2,X2),X) = f(neg(f(X2,X2)),X),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
f(f(and(X2,X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
neg(f(X,X)) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c208,plain,
f(neg(f(X2,X2)),X) = f(f(f(X2,X2),f(X2,X2)),X),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = f(f(f(f(X2,X2),f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
f(f(f(f(X2,X2),f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = X2,
inference(substitution,[status(thm)],[c33]) ).
cnf(c211,plain,
f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = X2,
inference(transitivity,[status(thm)],[c209,c210]) ).
cnf(c212,plain,
f(f(and(X2,X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = X2,
inference(transitivity,[status(thm)],[c206,c211]) ).
cnf(c213,plain,
f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = X2,
inference(transitivity,[status(thm)],[c202,c212]) ).
cnf(c214,plain,
f(f(neg(neg(X2)),neg(X)),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = X2,
inference(substitution,[status(thm)],[c213]) ).
cnf(c215,plain,
f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = X2,
inference(transitivity,[status(thm)],[c199,c214]) ).
cnf(c216,plain,
neg(f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))) = neg(X2),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
and(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = neg(X2),
inference(transitivity,[status(thm)],[c196,c216]) ).
cnf(c218,plain,
neg(X2) = and(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
or(neg(X2),and(or(neg(X2),X),neg(or(neg(X2),X)))) = or(and(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),and(or(neg(X2),X),neg(or(neg(X2),X)))),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
and(or(neg(X2),X),or(neg(X2),and(or(neg(X2),X),neg(or(neg(X2),X))))) = and(or(neg(X2),X),or(and(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),and(or(neg(X2),X),neg(or(neg(X2),X))))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c222,plain,
and(X,neg(X)) = and(neg(neg(X)),neg(X)),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
or(and(X2,X),and(X2,neg(X2))) = or(and(X2,X),and(neg(neg(X2)),neg(X2))),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
and(X2,or(and(X2,X),and(X2,neg(X2)))) = and(X2,or(and(X2,X),and(neg(neg(X2)),neg(X2)))),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
neg(or(neg(X),X)) = and(neg(neg(X)),neg(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c226,plain,
and(neg(neg(X)),neg(X)) = neg(or(neg(X),X)),
inference(symmetry,[status(thm)],[c225]) ).
cnf(c227,plain,
or(and(X2,X),and(neg(neg(X2)),neg(X2))) = or(and(X2,X),neg(or(neg(X2),X2))),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
and(X2,or(and(X2,X),and(neg(neg(X2)),neg(X2)))) = and(X2,or(and(X2,X),neg(or(neg(X2),X2)))),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c230,plain,
and(X2,X) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
or(and(X2,X),neg(or(neg(X2),X2))) = or(and(X2,neg(neg(X))),neg(or(neg(X2),X2))),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
and(X2,or(and(X2,X),neg(or(neg(X2),X2)))) = and(X2,or(and(X2,neg(neg(X))),neg(or(neg(X2),X2)))),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c234,plain,
and(X2,neg(neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
or(and(X2,neg(neg(X))),neg(or(neg(X2),X2))) = or(and(neg(neg(X2)),neg(neg(X))),neg(or(neg(X2),X2))),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
and(X2,or(and(X2,neg(neg(X))),neg(or(neg(X2),X2)))) = and(X2,or(and(neg(neg(X2)),neg(neg(X))),neg(or(neg(X2),X2)))),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
neg(or(neg(X2),neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c238,plain,
and(neg(neg(X2)),neg(neg(X))) = neg(or(neg(X2),neg(X))),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
or(and(neg(neg(X2)),neg(neg(X))),neg(or(neg(X2),X2))) = or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),X2))),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
and(X2,or(and(neg(neg(X2)),neg(neg(X))),neg(or(neg(X2),X2)))) = and(X2,or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),X2)))),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
f(or(neg(X2),neg(X)),or(neg(X2),X2)) = or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),X2))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c242,plain,
or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),X2))) = f(or(neg(X2),neg(X)),or(neg(X2),X2)),
inference(symmetry,[status(thm)],[c241]) ).
cnf(c243,plain,
and(X2,or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),X2)))) = and(X2,f(or(neg(X2),neg(X)),or(neg(X2),X2))),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
neg(and(or(neg(X2),neg(X)),or(neg(X2),X2))) = f(or(neg(X2),neg(X)),or(neg(X2),X2)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c245,plain,
f(or(neg(X2),neg(X)),or(neg(X2),X2)) = neg(and(or(neg(X2),neg(X)),or(neg(X2),X2))),
inference(symmetry,[status(thm)],[c244]) ).
cnf(c246,plain,
and(X2,f(or(neg(X2),neg(X)),or(neg(X2),X2))) = and(X2,neg(and(or(neg(X2),neg(X)),or(neg(X2),X2)))),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c248,plain,
and(X2,neg(and(or(neg(X2),neg(X)),or(neg(X2),X2)))) = and(neg(neg(X2)),neg(and(or(neg(X2),neg(X)),or(neg(X2),X2)))),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
neg(or(neg(X2),and(or(neg(X2),neg(X)),or(neg(X2),X2)))) = and(neg(neg(X2)),neg(and(or(neg(X2),neg(X)),or(neg(X2),X2)))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c250,plain,
and(neg(neg(X2)),neg(and(or(neg(X2),neg(X)),or(neg(X2),X2)))) = neg(or(neg(X2),and(or(neg(X2),neg(X)),or(neg(X2),X2)))),
inference(symmetry,[status(thm)],[c249]) ).
cnf(c251,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c252,plain,
or(neg(X),X) = or(neg(X),neg(neg(X))),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
and(or(neg(X2),neg(X)),or(neg(X2),X2)) = and(or(neg(X2),neg(X)),or(neg(X2),neg(neg(X2)))),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
or(neg(X2),and(or(neg(X2),neg(X)),or(neg(X2),X2))) = or(neg(X2),and(or(neg(X2),neg(X)),or(neg(X2),neg(neg(X2))))),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
neg(neg(X)) = and(X,X),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c256,plain,
or(neg(X),neg(neg(X))) = or(neg(X),and(X,X)),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
and(or(neg(X2),neg(X)),or(neg(X2),neg(neg(X2)))) = and(or(neg(X2),neg(X)),or(neg(X2),and(X2,X2))),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
or(neg(X2),and(or(neg(X2),neg(X)),or(neg(X2),neg(neg(X2))))) = or(neg(X2),and(or(neg(X2),neg(X)),or(neg(X2),and(X2,X2)))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
neg(neg(neg(X))) = neg(X),
inference(substitution,[status(thm)],[c79]) ).
cnf(c260,plain,
neg(X) = neg(neg(neg(X))),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
or(neg(X),and(X,X)) = or(neg(neg(neg(X))),and(X,X)),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
and(or(neg(X2),neg(X)),or(neg(X2),and(X2,X2))) = and(or(neg(X2),neg(X)),or(neg(neg(neg(X2))),and(X2,X2))),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
or(neg(X2),and(or(neg(X2),neg(X)),or(neg(X2),and(X2,X2)))) = or(neg(X2),and(or(neg(X2),neg(X)),or(neg(neg(neg(X2))),and(X2,X2)))),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
or(neg(X),neg(X)) = neg(neg(neg(X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c265,plain,
neg(neg(neg(X))) = or(neg(X),neg(X)),
inference(symmetry,[status(thm)],[c264]) ).
cnf(c266,plain,
or(neg(neg(neg(X))),and(X,X)) = or(or(neg(X),neg(X)),and(X,X)),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
and(or(neg(X2),neg(X)),or(neg(neg(neg(X2))),and(X2,X2))) = and(or(neg(X2),neg(X)),or(or(neg(X2),neg(X2)),and(X2,X2))),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
or(neg(X2),and(or(neg(X2),neg(X)),or(neg(neg(neg(X2))),and(X2,X2)))) = or(neg(X2),and(or(neg(X2),neg(X)),or(or(neg(X2),neg(X2)),and(X2,X2)))),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c270,plain,
and(X,X2) = and(X,neg(neg(X2))),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
or(or(neg(X),neg(X2)),and(X,X2)) = or(or(neg(X),neg(X2)),and(X,neg(neg(X2)))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))) = and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,neg(neg(X3))))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3)))) = or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,neg(neg(X3)))))),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c275,plain,
and(X,neg(neg(X2))) = and(neg(neg(X)),neg(neg(X2))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
or(or(neg(X),neg(X2)),and(X,neg(neg(X2)))) = or(or(neg(X),neg(X2)),and(neg(neg(X)),neg(neg(X2)))),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,neg(neg(X3))))) = and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(neg(neg(X)),neg(neg(X3))))),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,neg(neg(X3)))))) = or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(neg(neg(X)),neg(neg(X3)))))),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
neg(or(neg(X),neg(X2))) = and(neg(neg(X)),neg(neg(X2))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c280,plain,
and(neg(neg(X)),neg(neg(X2))) = neg(or(neg(X),neg(X2))),
inference(symmetry,[status(thm)],[c279]) ).
cnf(c281,plain,
or(or(neg(X),neg(X2)),and(neg(neg(X)),neg(neg(X2)))) = or(or(neg(X),neg(X2)),neg(or(neg(X),neg(X2)))),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(neg(neg(X)),neg(neg(X3))))) = and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),neg(or(neg(X),neg(X3))))),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(neg(neg(X)),neg(neg(X3)))))) = or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),neg(or(neg(X),neg(X3)))))),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
f(X,X2) = or(neg(X),neg(X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c285,plain,
or(neg(X),neg(X2)) = f(X,X2),
inference(symmetry,[status(thm)],[c284]) ).
cnf(c286,plain,
or(or(neg(X),neg(X2)),neg(or(neg(X),neg(X2)))) = or(f(X,X2),neg(or(neg(X),neg(X2)))),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),neg(or(neg(X),neg(X3))))) = and(or(neg(X3),neg(X2)),or(f(X,X3),neg(or(neg(X),neg(X3))))),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),neg(or(neg(X),neg(X3)))))) = or(neg(X3),and(or(neg(X3),neg(X2)),or(f(X,X3),neg(or(neg(X),neg(X3)))))),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
f(X,X2) = or(neg(X),neg(X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c290,plain,
or(neg(X),neg(X2)) = f(X,X2),
inference(symmetry,[status(thm)],[c289]) ).
cnf(c291,plain,
neg(or(neg(X),neg(X2))) = neg(f(X,X2)),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
or(f(X,X2),neg(or(neg(X),neg(X2)))) = or(f(X,X2),neg(f(X,X2))),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
and(or(neg(X3),neg(X2)),or(f(X,X3),neg(or(neg(X),neg(X3))))) = and(or(neg(X3),neg(X2)),or(f(X,X3),neg(f(X,X3)))),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(f(X,X3),neg(or(neg(X),neg(X3)))))) = or(neg(X3),and(or(neg(X3),neg(X2)),or(f(X,X3),neg(f(X,X3))))),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
neg(and(X,X2)) = f(X,X2),
inference(substitution,[status(thm)],[c105]) ).
cnf(c296,plain,
f(X,X2) = neg(and(X,X2)),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
or(f(X,X2),neg(f(X,X2))) = or(neg(and(X,X2)),neg(f(X,X2))),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
and(or(neg(X3),neg(X2)),or(f(X,X3),neg(f(X,X3)))) = and(or(neg(X3),neg(X2)),or(neg(and(X,X3)),neg(f(X,X3)))),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(f(X,X3),neg(f(X,X3))))) = or(neg(X3),and(or(neg(X3),neg(X2)),or(neg(and(X,X3)),neg(f(X,X3))))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
f(and(X,X2),f(X,X2)) = or(neg(and(X,X2)),neg(f(X,X2))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c301,plain,
or(neg(and(X,X2)),neg(f(X,X2))) = f(and(X,X2),f(X,X2)),
inference(symmetry,[status(thm)],[c300]) ).
cnf(c302,plain,
and(or(neg(X3),neg(X2)),or(neg(and(X,X3)),neg(f(X,X3)))) = and(or(neg(X3),neg(X2)),f(and(X,X3),f(X,X3))),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(neg(and(X,X3)),neg(f(X,X3))))) = or(neg(X3),and(or(neg(X3),neg(X2)),f(and(X,X3),f(X,X3)))),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
or(neg(X2),neg(X)) = f(X2,X),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c305,plain,
and(or(neg(X3),neg(X2)),f(and(X,X3),f(X,X3))) = and(f(X3,X2),f(and(X,X3),f(X,X3))),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),f(and(X,X3),f(X,X3)))) = or(neg(X3),and(f(X3,X2),f(and(X,X3),f(X,X3)))),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
neg(f(f(X3,X2),f(and(X,X3),f(X,X3)))) = and(f(X3,X2),f(and(X,X3),f(X,X3))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c308,plain,
and(f(X3,X2),f(and(X,X3),f(X,X3))) = neg(f(f(X3,X2),f(and(X,X3),f(X,X3)))),
inference(symmetry,[status(thm)],[c307]) ).
cnf(c309,plain,
or(neg(X3),and(f(X3,X2),f(and(X,X3),f(X,X3)))) = or(neg(X3),neg(f(f(X3,X2),f(and(X,X3),f(X,X3))))),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
f(X3,f(f(X3,X2),f(and(X,X3),f(X,X3)))) = or(neg(X3),neg(f(f(X3,X2),f(and(X,X3),f(X,X3))))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c311,plain,
or(neg(X3),neg(f(f(X3,X2),f(and(X,X3),f(X,X3))))) = f(X3,f(f(X3,X2),f(and(X,X3),f(X,X3)))),
inference(symmetry,[status(thm)],[c310]) ).
cnf(c312,plain,
f(f(X4,X3),f(f(f(X4,X3),f(and(X2,X4),f(X2,X4))),f(f(f(f(X4,X3),f(and(X2,X4),f(X2,X4))),f(and(X,f(X4,X3)),f(X,f(X4,X3)))),X5))) = f(f(X4,X3),f(and(X2,X4),f(X2,X4))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c313,plain,
f(f(X5,X4),f(and(X3,X5),f(X3,X5))) = f(f(X5,X4),f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(and(X2,f(X5,X4)),f(X2,f(X5,X4)))),X))),
inference(symmetry,[status(thm)],[c312]) ).
cnf(c314,plain,
f(X5,f(f(X5,X4),f(and(X3,X5),f(X3,X5)))) = f(X5,f(f(X5,X4),f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(and(X2,f(X5,X4)),f(X2,f(X5,X4)))),X)))),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
f(X5,f(f(X5,X4),f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(and(X2,f(X5,X4)),f(X2,f(X5,X4)))),X)))) = f(X5,X4),
inference(substitution,[status(thm)],[c59]) ).
cnf(c316,plain,
f(X5,f(f(X5,X4),f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(and(X2,f(X5,X4)),f(X2,f(X5,X4)))),X)))) = or(neg(X5),neg(X4)),
inference(transitivity,[status(thm)],[c315,c87]) ).
cnf(c317,plain,
f(X3,f(f(X3,X2),f(and(X,X3),f(X,X3)))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c314,c316]) ).
cnf(c318,plain,
or(neg(X3),neg(f(f(X3,X2),f(and(X,X3),f(X,X3))))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c311,c317]) ).
cnf(c319,plain,
or(neg(X3),and(f(X3,X2),f(and(X,X3),f(X,X3)))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c309,c318]) ).
cnf(c320,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),f(and(X,X3),f(X,X3)))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c306,c319]) ).
cnf(c321,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(neg(and(X,X3)),neg(f(X,X3))))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c303,c320]) ).
cnf(c322,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(f(X,X3),neg(f(X,X3))))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c299,c321]) ).
cnf(c323,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(f(X,X3),neg(or(neg(X),neg(X3)))))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c294,c322]) ).
cnf(c324,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),neg(or(neg(X),neg(X3)))))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c288,c323]) ).
cnf(c325,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(neg(neg(X)),neg(neg(X3)))))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c283,c324]) ).
cnf(c326,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,neg(neg(X3)))))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c278,c325]) ).
cnf(c327,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3)))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c273,c326]) ).
cnf(c328,plain,
or(neg(X2),and(or(neg(X2),neg(X)),or(or(neg(X2),neg(X2)),and(X2,X2)))) = or(neg(X2),neg(X)),
inference(substitution,[status(thm)],[c327]) ).
cnf(c329,plain,
or(neg(X2),and(or(neg(X2),neg(X)),or(neg(neg(neg(X2))),and(X2,X2)))) = or(neg(X2),neg(X)),
inference(transitivity,[status(thm)],[c268,c328]) ).
cnf(c330,plain,
or(neg(X2),and(or(neg(X2),neg(X)),or(neg(X2),and(X2,X2)))) = or(neg(X2),neg(X)),
inference(transitivity,[status(thm)],[c263,c329]) ).
cnf(c331,plain,
or(neg(X2),and(or(neg(X2),neg(X)),or(neg(X2),neg(neg(X2))))) = or(neg(X2),neg(X)),
inference(transitivity,[status(thm)],[c258,c330]) ).
cnf(c332,plain,
or(neg(X2),and(or(neg(X2),neg(X)),or(neg(X2),X2))) = or(neg(X2),neg(X)),
inference(transitivity,[status(thm)],[c254,c331]) ).
cnf(c333,plain,
neg(or(neg(X2),and(or(neg(X2),neg(X)),or(neg(X2),X2)))) = neg(or(neg(X2),neg(X))),
inference(congruence,[status(thm)],[c332]) ).
cnf(c334,plain,
neg(or(neg(X2),neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c335,plain,
and(neg(neg(X2)),neg(neg(X))) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c336,plain,
and(X2,neg(neg(X))) = and(X2,X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c337,plain,
and(neg(neg(X2)),neg(neg(X))) = and(X2,X),
inference(transitivity,[status(thm)],[c335,c336]) ).
cnf(c338,plain,
neg(or(neg(X2),neg(X))) = and(X2,X),
inference(transitivity,[status(thm)],[c334,c337]) ).
cnf(c339,plain,
neg(or(neg(X2),and(or(neg(X2),neg(X)),or(neg(X2),X2)))) = and(X2,X),
inference(transitivity,[status(thm)],[c333,c338]) ).
cnf(c340,plain,
and(neg(neg(X2)),neg(and(or(neg(X2),neg(X)),or(neg(X2),X2)))) = and(X2,X),
inference(transitivity,[status(thm)],[c250,c339]) ).
cnf(c341,plain,
and(X2,neg(and(or(neg(X2),neg(X)),or(neg(X2),X2)))) = and(X2,X),
inference(transitivity,[status(thm)],[c248,c340]) ).
cnf(c342,plain,
and(X2,f(or(neg(X2),neg(X)),or(neg(X2),X2))) = and(X2,X),
inference(transitivity,[status(thm)],[c246,c341]) ).
cnf(c343,plain,
and(X2,or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),X2)))) = and(X2,X),
inference(transitivity,[status(thm)],[c243,c342]) ).
cnf(c344,plain,
and(X2,or(and(neg(neg(X2)),neg(neg(X))),neg(or(neg(X2),X2)))) = and(X2,X),
inference(transitivity,[status(thm)],[c240,c343]) ).
cnf(c345,plain,
and(X2,or(and(X2,neg(neg(X))),neg(or(neg(X2),X2)))) = and(X2,X),
inference(transitivity,[status(thm)],[c236,c344]) ).
cnf(c346,plain,
and(X2,or(and(X2,X),neg(or(neg(X2),X2)))) = and(X2,X),
inference(transitivity,[status(thm)],[c232,c345]) ).
cnf(c347,plain,
and(X2,or(and(X2,X),and(neg(neg(X2)),neg(X2)))) = and(X2,X),
inference(transitivity,[status(thm)],[c228,c346]) ).
cnf(c348,plain,
and(X2,or(and(X2,X),and(X2,neg(X2)))) = and(X2,X),
inference(transitivity,[status(thm)],[c224,c347]) ).
cnf(c349,plain,
and(or(neg(X2),X),or(and(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),and(or(neg(X2),X),neg(or(neg(X2),X))))) = and(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(substitution,[status(thm)],[c348]) ).
cnf(c350,plain,
and(or(neg(X2),X),or(and(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),and(or(neg(X2),X),neg(or(neg(X2),X))))) = neg(X2),
inference(transitivity,[status(thm)],[c349,c217]) ).
cnf(c351,plain,
and(or(neg(X2),X),or(neg(X2),and(or(neg(X2),X),neg(or(neg(X2),X))))) = neg(X2),
inference(transitivity,[status(thm)],[c220,c350]) ).
cnf(c352,plain,
and(or(neg(X2),X),or(neg(X2),and(or(neg(X2),X),and(neg(neg(X2)),neg(X))))) = neg(X2),
inference(transitivity,[status(thm)],[c194,c351]) ).
cnf(c353,plain,
and(or(neg(X2),X),or(neg(X2),and(or(neg(X2),X),and(X2,neg(X))))) = neg(X2),
inference(transitivity,[status(thm)],[c189,c352]) ).
cnf(c354,plain,
and(or(neg(neg(X2)),X),or(neg(neg(X2)),and(or(neg(neg(X2)),X),and(neg(X2),neg(X))))) = neg(neg(X2)),
inference(substitution,[status(thm)],[c353]) ).
cnf(c355,plain,
and(or(neg(neg(X2)),X),or(neg(neg(X2)),and(or(neg(neg(X2)),X),and(neg(X2),neg(X))))) = X2,
inference(transitivity,[status(thm)],[c354,c79]) ).
cnf(c356,plain,
and(or(X2,X),or(neg(neg(X2)),and(or(neg(neg(X2)),X),and(neg(X2),neg(X))))) = X2,
inference(transitivity,[status(thm)],[c184,c355]) ).
cnf(c357,plain,
and(or(X2,X),or(neg(neg(X2)),and(or(X2,X),and(neg(X2),neg(X))))) = X2,
inference(transitivity,[status(thm)],[c181,c356]) ).
cnf(c358,plain,
and(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X))))) = X2,
inference(transitivity,[status(thm)],[c176,c357]) ).
cnf(c359,plain,
X2 = and(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X))))),
inference(symmetry,[status(thm)],[c358]) ).
cnf(c360,plain,
and(or(X2,X),X2) = and(or(X2,X),and(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X)))))),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
neg(neg(and(X2,X))) = and(X2,X),
inference(substitution,[status(thm)],[c79]) ).
cnf(c362,plain,
and(X2,X) = neg(neg(and(X2,X))),
inference(symmetry,[status(thm)],[c361]) ).
cnf(c363,plain,
and(X2,and(X2,X)) = and(X2,neg(neg(and(X2,X)))),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
or(and(X2,X),and(X2,X)) = neg(neg(and(X2,X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c365,plain,
neg(neg(and(X2,X))) = or(and(X2,X),and(X2,X)),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
and(X2,neg(neg(and(X2,X)))) = and(X2,or(and(X2,X),and(X2,X))),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
and(or(and(X2,X),and(X2,neg(X2))),or(and(X2,X),and(or(and(X2,X),and(X2,neg(X2))),and(neg(and(X2,X)),neg(and(X2,neg(X2))))))) = and(X2,X),
inference(substitution,[status(thm)],[c358]) ).
cnf(c368,plain,
and(X2,X) = and(or(and(X2,X),and(X2,neg(X2))),or(and(X2,X),and(or(and(X2,X),and(X2,neg(X2))),and(neg(and(X2,X)),neg(and(X2,neg(X2))))))),
inference(symmetry,[status(thm)],[c367]) ).
cnf(c369,plain,
or(and(X2,X),and(X2,X)) = or(and(X2,X),and(or(and(X2,X),and(X2,neg(X2))),or(and(X2,X),and(or(and(X2,X),and(X2,neg(X2))),and(neg(and(X2,X)),neg(and(X2,neg(X2)))))))),
inference(congruence,[status(thm)],[c368]) ).
cnf(c370,plain,
and(X2,or(and(X2,X),and(X2,X))) = and(X2,or(and(X2,X),and(or(and(X2,X),and(X2,neg(X2))),or(and(X2,X),and(or(and(X2,X),and(X2,neg(X2))),and(neg(and(X2,X)),neg(and(X2,neg(X2))))))))),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c372,plain,
and(or(and(X3,X2),and(X3,neg(X3))),X) = and(or(and(X3,X2),and(X3,neg(X3))),neg(neg(X))),
inference(congruence,[status(thm)],[c371]) ).
cnf(c373,plain,
or(and(X3,X2),and(or(and(X3,X2),and(X3,neg(X3))),X)) = or(and(X3,X2),and(or(and(X3,X2),and(X3,neg(X3))),neg(neg(X)))),
inference(congruence,[status(thm)],[c372]) ).
cnf(c374,plain,
and(X3,or(and(X3,X2),and(or(and(X3,X2),and(X3,neg(X3))),X))) = and(X3,or(and(X3,X2),and(or(and(X3,X2),and(X3,neg(X3))),neg(neg(X))))),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c376,plain,
and(X,neg(X)) = and(neg(neg(X)),neg(X)),
inference(congruence,[status(thm)],[c375]) ).
cnf(c377,plain,
or(and(X2,X),and(X2,neg(X2))) = or(and(X2,X),and(neg(neg(X2)),neg(X2))),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
and(or(and(X3,X2),and(X3,neg(X3))),neg(neg(X))) = and(or(and(X3,X2),and(neg(neg(X3)),neg(X3))),neg(neg(X))),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
or(and(X3,X2),and(or(and(X3,X2),and(X3,neg(X3))),neg(neg(X)))) = or(and(X3,X2),and(or(and(X3,X2),and(neg(neg(X3)),neg(X3))),neg(neg(X)))),
inference(congruence,[status(thm)],[c378]) ).
cnf(c380,plain,
and(X3,or(and(X3,X2),and(or(and(X3,X2),and(X3,neg(X3))),neg(neg(X))))) = and(X3,or(and(X3,X2),and(or(and(X3,X2),and(neg(neg(X3)),neg(X3))),neg(neg(X))))),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
neg(or(neg(X),X)) = and(neg(neg(X)),neg(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c382,plain,
and(neg(neg(X)),neg(X)) = neg(or(neg(X),X)),
inference(symmetry,[status(thm)],[c381]) ).
cnf(c383,plain,
or(and(X2,X),and(neg(neg(X2)),neg(X2))) = or(and(X2,X),neg(or(neg(X2),X2))),
inference(congruence,[status(thm)],[c382]) ).
cnf(c384,plain,
and(or(and(X3,X2),and(neg(neg(X3)),neg(X3))),neg(neg(X))) = and(or(and(X3,X2),neg(or(neg(X3),X3))),neg(neg(X))),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,plain,
or(and(X3,X2),and(or(and(X3,X2),and(neg(neg(X3)),neg(X3))),neg(neg(X)))) = or(and(X3,X2),and(or(and(X3,X2),neg(or(neg(X3),X3))),neg(neg(X)))),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
and(X3,or(and(X3,X2),and(or(and(X3,X2),and(neg(neg(X3)),neg(X3))),neg(neg(X))))) = and(X3,or(and(X3,X2),and(or(and(X3,X2),neg(or(neg(X3),X3))),neg(neg(X))))),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c388,plain,
and(X2,X) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c387]) ).
cnf(c389,plain,
or(and(X2,X),neg(or(neg(X2),X2))) = or(and(X2,neg(neg(X))),neg(or(neg(X2),X2))),
inference(congruence,[status(thm)],[c388]) ).
cnf(c390,plain,
and(or(and(X3,X2),neg(or(neg(X3),X3))),neg(neg(X))) = and(or(and(X3,neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
or(and(X3,X2),and(or(and(X3,X2),neg(or(neg(X3),X3))),neg(neg(X)))) = or(and(X3,X2),and(or(and(X3,neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X)))),
inference(congruence,[status(thm)],[c390]) ).
cnf(c392,plain,
and(X3,or(and(X3,X2),and(or(and(X3,X2),neg(or(neg(X3),X3))),neg(neg(X))))) = and(X3,or(and(X3,X2),and(or(and(X3,neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))))),
inference(congruence,[status(thm)],[c391]) ).
cnf(c393,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c394,plain,
and(X2,neg(neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
or(and(X2,neg(neg(X))),neg(or(neg(X2),X2))) = or(and(neg(neg(X2)),neg(neg(X))),neg(or(neg(X2),X2))),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
and(or(and(X3,neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))) = and(or(and(neg(neg(X3)),neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
or(and(X3,X2),and(or(and(X3,neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X)))) = or(and(X3,X2),and(or(and(neg(neg(X3)),neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X)))),
inference(congruence,[status(thm)],[c396]) ).
cnf(c398,plain,
and(X3,or(and(X3,X2),and(or(and(X3,neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))))) = and(X3,or(and(X3,X2),and(or(and(neg(neg(X3)),neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))))),
inference(congruence,[status(thm)],[c397]) ).
cnf(c399,plain,
neg(or(neg(X2),neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c400,plain,
and(neg(neg(X2)),neg(neg(X))) = neg(or(neg(X2),neg(X))),
inference(symmetry,[status(thm)],[c399]) ).
cnf(c401,plain,
or(and(neg(neg(X2)),neg(neg(X))),neg(or(neg(X2),X2))) = or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),X2))),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
and(or(and(neg(neg(X3)),neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))) = and(or(neg(or(neg(X3),neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))),
inference(congruence,[status(thm)],[c401]) ).
cnf(c403,plain,
or(and(X3,X2),and(or(and(neg(neg(X3)),neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X)))) = or(and(X3,X2),and(or(neg(or(neg(X3),neg(X2))),neg(or(neg(X3),X3))),neg(neg(X)))),
inference(congruence,[status(thm)],[c402]) ).
cnf(c404,plain,
and(X3,or(and(X3,X2),and(or(and(neg(neg(X3)),neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))))) = and(X3,or(and(X3,X2),and(or(neg(or(neg(X3),neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))))),
inference(congruence,[status(thm)],[c403]) ).
cnf(c405,plain,
f(or(neg(X2),neg(X)),or(neg(X2),X2)) = or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),X2))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c406,plain,
or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),X2))) = f(or(neg(X2),neg(X)),or(neg(X2),X2)),
inference(symmetry,[status(thm)],[c405]) ).
cnf(c407,plain,
and(or(neg(or(neg(X3),neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))) = and(f(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(neg(X))),
inference(congruence,[status(thm)],[c406]) ).
cnf(c408,plain,
or(and(X3,X2),and(or(neg(or(neg(X3),neg(X2))),neg(or(neg(X3),X3))),neg(neg(X)))) = or(and(X3,X2),and(f(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(neg(X)))),
inference(congruence,[status(thm)],[c407]) ).
cnf(c409,plain,
and(X3,or(and(X3,X2),and(or(neg(or(neg(X3),neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))))) = and(X3,or(and(X3,X2),and(f(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(neg(X))))),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,plain,
neg(and(or(neg(X2),neg(X)),or(neg(X2),X2))) = f(or(neg(X2),neg(X)),or(neg(X2),X2)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c411,plain,
f(or(neg(X2),neg(X)),or(neg(X2),X2)) = neg(and(or(neg(X2),neg(X)),or(neg(X2),X2))),
inference(symmetry,[status(thm)],[c410]) ).
cnf(c412,plain,
and(f(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(neg(X))) = and(neg(and(or(neg(X3),neg(X2)),or(neg(X3),X3))),neg(neg(X))),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
or(and(X3,X2),and(f(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(neg(X)))) = or(and(X3,X2),and(neg(and(or(neg(X3),neg(X2)),or(neg(X3),X3))),neg(neg(X)))),
inference(congruence,[status(thm)],[c412]) ).
cnf(c414,plain,
and(X3,or(and(X3,X2),and(f(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(neg(X))))) = and(X3,or(and(X3,X2),and(neg(and(or(neg(X3),neg(X2)),or(neg(X3),X3))),neg(neg(X))))),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))) = and(neg(and(or(neg(X3),neg(X2)),or(neg(X3),X3))),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c416,plain,
and(neg(and(or(neg(X3),neg(X2)),or(neg(X3),X3))),neg(neg(X))) = neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))),
inference(symmetry,[status(thm)],[c415]) ).
cnf(c417,plain,
or(and(X3,X2),and(neg(and(or(neg(X3),neg(X2)),or(neg(X3),X3))),neg(neg(X)))) = or(and(X3,X2),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))),
inference(congruence,[status(thm)],[c416]) ).
cnf(c418,plain,
and(X3,or(and(X3,X2),and(neg(and(or(neg(X3),neg(X2)),or(neg(X3),X3))),neg(neg(X))))) = and(X3,or(and(X3,X2),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))),
inference(congruence,[status(thm)],[c417]) ).
cnf(c419,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c420,plain,
and(X2,X) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c419]) ).
cnf(c421,plain,
or(and(X3,X2),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))) = or(and(X3,neg(neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
and(X3,or(and(X3,X2),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(X3,or(and(X3,neg(neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))),
inference(congruence,[status(thm)],[c421]) ).
cnf(c423,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c424,plain,
and(X2,neg(neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(congruence,[status(thm)],[c423]) ).
cnf(c425,plain,
or(and(X3,neg(neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))) = or(and(neg(neg(X3)),neg(neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))),
inference(congruence,[status(thm)],[c424]) ).
cnf(c426,plain,
and(X3,or(and(X3,neg(neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(X3,or(and(neg(neg(X3)),neg(neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))),
inference(congruence,[status(thm)],[c425]) ).
cnf(c427,plain,
neg(or(neg(X2),neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c428,plain,
and(neg(neg(X2)),neg(neg(X))) = neg(or(neg(X2),neg(X))),
inference(symmetry,[status(thm)],[c427]) ).
cnf(c429,plain,
or(and(neg(neg(X3)),neg(neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))) = or(neg(or(neg(X3),neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
and(X3,or(and(neg(neg(X3)),neg(neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(X3,or(neg(or(neg(X3),neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))),
inference(congruence,[status(thm)],[c429]) ).
cnf(c431,plain,
f(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))) = or(neg(or(neg(X3),neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c432,plain,
or(neg(or(neg(X3),neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))) = f(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))),
inference(symmetry,[status(thm)],[c431]) ).
cnf(c433,plain,
and(X3,or(neg(or(neg(X3),neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(X3,f(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))),
inference(congruence,[status(thm)],[c432]) ).
cnf(c434,plain,
neg(and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))) = f(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c435,plain,
f(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))) = neg(and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))),
inference(symmetry,[status(thm)],[c434]) ).
cnf(c436,plain,
and(X3,f(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))) = and(X3,neg(and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c438,plain,
and(X3,neg(and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(neg(neg(X3)),neg(and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))),
inference(congruence,[status(thm)],[c437]) ).
cnf(c439,plain,
neg(or(neg(X3),and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(neg(neg(X3)),neg(and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c440,plain,
and(neg(neg(X3)),neg(and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = neg(or(neg(X3),and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))),
inference(symmetry,[status(thm)],[c439]) ).
cnf(c441,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c442,plain,
or(neg(X),X) = or(f(X,X),X),
inference(congruence,[status(thm)],[c441]) ).
cnf(c443,plain,
and(or(neg(X2),neg(X)),or(neg(X2),X2)) = and(or(neg(X2),neg(X)),or(f(X2,X2),X2)),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)) = or(and(or(neg(X3),neg(X2)),or(f(X3,X3),X3)),neg(X)),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))) = and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(f(X3,X3),X3)),neg(X))),
inference(congruence,[status(thm)],[c444]) ).
cnf(c446,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))) = or(neg(X3),and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(f(X3,X3),X3)),neg(X)))),
inference(congruence,[status(thm)],[c445]) ).
cnf(c447,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c448,plain,
f(and(X3,X2),neg(X)) = f(neg(f(X3,X2)),neg(X)),
inference(congruence,[status(thm)],[c447]) ).
cnf(c449,plain,
f(neg(f(X3,X2)),neg(X)) = or(f(X3,X2),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c450,plain,
f(and(X3,X2),neg(X)) = or(f(X3,X2),X),
inference(transitivity,[status(thm)],[c448,c449]) ).
cnf(c451,plain,
f(and(X,X),neg(X)) = or(f(X,X),X),
inference(substitution,[status(thm)],[c450]) ).
cnf(c452,plain,
or(f(X,X),X) = f(and(X,X),neg(X)),
inference(symmetry,[status(thm)],[c451]) ).
cnf(c453,plain,
and(or(neg(X2),neg(X)),or(f(X2,X2),X2)) = and(or(neg(X2),neg(X)),f(and(X2,X2),neg(X2))),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
or(and(or(neg(X3),neg(X2)),or(f(X3,X3),X3)),neg(X)) = or(and(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),neg(X)),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(f(X3,X3),X3)),neg(X))) = and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),neg(X))),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(f(X3,X3),X3)),neg(X)))) = or(neg(X3),and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),neg(X)))),
inference(congruence,[status(thm)],[c455]) ).
cnf(c457,plain,
neg(f(or(neg(X2),neg(X)),f(and(X2,X2),neg(X2)))) = and(or(neg(X2),neg(X)),f(and(X2,X2),neg(X2))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c458,plain,
and(or(neg(X2),neg(X)),f(and(X2,X2),neg(X2))) = neg(f(or(neg(X2),neg(X)),f(and(X2,X2),neg(X2)))),
inference(symmetry,[status(thm)],[c457]) ).
cnf(c459,plain,
or(and(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),neg(X)) = or(neg(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3)))),neg(X)),
inference(congruence,[status(thm)],[c458]) ).
cnf(c460,plain,
and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),neg(X))) = and(or(neg(X3),neg(X2)),or(neg(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3)))),neg(X))),
inference(congruence,[status(thm)],[c459]) ).
cnf(c461,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),neg(X)))) = or(neg(X3),and(or(neg(X3),neg(X2)),or(neg(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3)))),neg(X)))),
inference(congruence,[status(thm)],[c460]) ).
cnf(c462,plain,
f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X) = or(neg(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3)))),neg(X)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c463,plain,
or(neg(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3)))),neg(X)) = f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X),
inference(symmetry,[status(thm)],[c462]) ).
cnf(c464,plain,
and(or(neg(X3),neg(X2)),or(neg(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3)))),neg(X))) = and(or(neg(X3),neg(X2)),f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X)),
inference(congruence,[status(thm)],[c463]) ).
cnf(c465,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(neg(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3)))),neg(X)))) = or(neg(X3),and(or(neg(X3),neg(X2)),f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X))),
inference(congruence,[status(thm)],[c464]) ).
cnf(c466,plain,
or(neg(X2),neg(X)) = f(X2,X),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c467,plain,
and(or(neg(X3),neg(X2)),f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X)) = and(f(X3,X2),f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X)),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X))) = or(neg(X3),and(f(X3,X2),f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X))),
inference(congruence,[status(thm)],[c467]) ).
cnf(c469,plain,
or(neg(X2),neg(X)) = f(X2,X),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c470,plain,
f(or(neg(X2),neg(X)),f(and(X2,X2),neg(X2))) = f(f(X2,X),f(and(X2,X2),neg(X2))),
inference(congruence,[status(thm)],[c469]) ).
cnf(c471,plain,
f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X) = f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X),
inference(congruence,[status(thm)],[c470]) ).
cnf(c472,plain,
and(f(X3,X2),f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X)) = and(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X)),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
or(neg(X3),and(f(X3,X2),f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X))) = or(neg(X3),and(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X))),
inference(congruence,[status(thm)],[c472]) ).
cnf(c474,plain,
neg(f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X))) = and(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c475,plain,
and(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X)) = neg(f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X))),
inference(symmetry,[status(thm)],[c474]) ).
cnf(c476,plain,
or(neg(X3),and(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X))) = or(neg(X3),neg(f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X)))),
inference(congruence,[status(thm)],[c475]) ).
cnf(c477,plain,
f(X3,f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X))) = or(neg(X3),neg(f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c478,plain,
or(neg(X3),neg(f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X)))) = f(X3,f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X))),
inference(symmetry,[status(thm)],[c477]) ).
cnf(c479,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c480,plain,
f(and(X,X),neg(X)) = f(and(X,X),f(X,X)),
inference(congruence,[status(thm)],[c479]) ).
cnf(c481,plain,
f(f(X2,X),f(and(X2,X2),neg(X2))) = f(f(X2,X),f(and(X2,X2),f(X2,X2))),
inference(congruence,[status(thm)],[c480]) ).
cnf(c482,plain,
f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X) = f(f(f(X3,X2),f(and(X3,X3),f(X3,X3))),X),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X)) = f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),f(X3,X3))),X)),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
f(X3,f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X))) = f(X3,f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),f(X3,X3))),X))),
inference(congruence,[status(thm)],[c483]) ).
cnf(c485,plain,
f(X3,f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),f(X3,X3))),X))) = f(X3,X2),
inference(substitution,[status(thm)],[c59]) ).
cnf(c486,plain,
f(X3,f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),f(X3,X3))),X))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c485,c87]) ).
cnf(c487,plain,
f(X3,f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c484,c486]) ).
cnf(c488,plain,
or(neg(X3),neg(f(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X)))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c478,c487]) ).
cnf(c489,plain,
or(neg(X3),and(f(X3,X2),f(f(f(X3,X2),f(and(X3,X3),neg(X3))),X))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c476,c488]) ).
cnf(c490,plain,
or(neg(X3),and(f(X3,X2),f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c473,c489]) ).
cnf(c491,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),f(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),X))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c468,c490]) ).
cnf(c492,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(neg(f(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3)))),neg(X)))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c465,c491]) ).
cnf(c493,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),f(and(X3,X3),neg(X3))),neg(X)))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c461,c492]) ).
cnf(c494,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(f(X3,X3),X3)),neg(X)))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c456,c493]) ).
cnf(c495,plain,
or(neg(X3),and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))) = or(neg(X3),neg(X2)),
inference(transitivity,[status(thm)],[c446,c494]) ).
cnf(c496,plain,
neg(or(neg(X3),and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = neg(or(neg(X3),neg(X2))),
inference(congruence,[status(thm)],[c495]) ).
cnf(c497,plain,
neg(or(neg(X2),neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c498,plain,
and(neg(neg(X2)),neg(neg(X))) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c499,plain,
and(X2,neg(neg(X))) = and(X2,X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c500,plain,
and(neg(neg(X2)),neg(neg(X))) = and(X2,X),
inference(transitivity,[status(thm)],[c498,c499]) ).
cnf(c501,plain,
neg(or(neg(X2),neg(X))) = and(X2,X),
inference(transitivity,[status(thm)],[c497,c500]) ).
cnf(c502,plain,
neg(or(neg(X3),and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c496,c501]) ).
cnf(c503,plain,
and(neg(neg(X3)),neg(and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c440,c502]) ).
cnf(c504,plain,
and(X3,neg(and(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c438,c503]) ).
cnf(c505,plain,
and(X3,f(or(neg(X3),neg(X2)),or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X)))) = and(X3,X2),
inference(transitivity,[status(thm)],[c436,c504]) ).
cnf(c506,plain,
and(X3,or(neg(or(neg(X3),neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c433,c505]) ).
cnf(c507,plain,
and(X3,or(and(neg(neg(X3)),neg(neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c430,c506]) ).
cnf(c508,plain,
and(X3,or(and(X3,neg(neg(X2))),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c426,c507]) ).
cnf(c509,plain,
and(X3,or(and(X3,X2),neg(or(and(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c422,c508]) ).
cnf(c510,plain,
and(X3,or(and(X3,X2),and(neg(and(or(neg(X3),neg(X2)),or(neg(X3),X3))),neg(neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c418,c509]) ).
cnf(c511,plain,
and(X3,or(and(X3,X2),and(f(or(neg(X3),neg(X2)),or(neg(X3),X3)),neg(neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c414,c510]) ).
cnf(c512,plain,
and(X3,or(and(X3,X2),and(or(neg(or(neg(X3),neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c409,c511]) ).
cnf(c513,plain,
and(X3,or(and(X3,X2),and(or(and(neg(neg(X3)),neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c404,c512]) ).
cnf(c514,plain,
and(X3,or(and(X3,X2),and(or(and(X3,neg(neg(X2))),neg(or(neg(X3),X3))),neg(neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c398,c513]) ).
cnf(c515,plain,
and(X3,or(and(X3,X2),and(or(and(X3,X2),neg(or(neg(X3),X3))),neg(neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c392,c514]) ).
cnf(c516,plain,
and(X3,or(and(X3,X2),and(or(and(X3,X2),and(neg(neg(X3)),neg(X3))),neg(neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c386,c515]) ).
cnf(c517,plain,
and(X3,or(and(X3,X2),and(or(and(X3,X2),and(X3,neg(X3))),neg(neg(X))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c380,c516]) ).
cnf(c518,plain,
and(X3,or(and(X3,X2),and(or(and(X3,X2),and(X3,neg(X3))),X))) = and(X3,X2),
inference(transitivity,[status(thm)],[c374,c517]) ).
cnf(c519,plain,
and(X2,or(and(X2,X),and(or(and(X2,X),and(X2,neg(X2))),or(and(X2,X),and(or(and(X2,X),and(X2,neg(X2))),and(neg(and(X2,X)),neg(and(X2,neg(X2))))))))) = and(X2,X),
inference(substitution,[status(thm)],[c518]) ).
cnf(c520,plain,
and(X2,or(and(X2,X),and(X2,X))) = and(X2,X),
inference(transitivity,[status(thm)],[c370,c519]) ).
cnf(c521,plain,
and(X2,neg(neg(and(X2,X)))) = and(X2,X),
inference(transitivity,[status(thm)],[c366,c520]) ).
cnf(c522,plain,
and(X2,and(X2,X)) = and(X2,X),
inference(transitivity,[status(thm)],[c363,c521]) ).
cnf(c523,plain,
and(or(X2,X),and(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X)))))) = and(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X))))),
inference(substitution,[status(thm)],[c522]) ).
cnf(c524,plain,
and(or(X2,X),and(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X)))))) = X2,
inference(transitivity,[status(thm)],[c523,c358]) ).
cnf(c525,plain,
and(or(X2,X),X2) = X2,
inference(transitivity,[status(thm)],[c360,c524]) ).
cnf(c526,plain,
and(or(or(and(X2,X3),and(X3,X)),and(X3,or(and(X3,or(X2,neg(X2))),neg(X)))),or(and(X2,X3),and(X3,X))) = or(and(X2,X3),and(X3,X)),
inference(substitution,[status(thm)],[c525]) ).
cnf(c527,plain,
and(X3,or(and(X2,X3),and(X3,X))) = or(and(X2,X3),and(X3,X)),
inference(transitivity,[status(thm)],[c173,c526]) ).
cnf(c528,plain,
and(X2,or(and(X,X2),and(X2,X2))) = or(and(X,X2),and(X2,X2)),
inference(substitution,[status(thm)],[c527]) ).
cnf(c529,plain,
or(and(X,X2),and(X2,X2)) = or(and(X,X2),neg(neg(X2))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c530,plain,
or(and(X,X2),neg(neg(X2))) = or(and(X,X2),X2),
inference(congruence,[status(thm)],[c79]) ).
cnf(c531,plain,
or(and(X,X2),and(X2,X2)) = or(and(X,X2),X2),
inference(transitivity,[status(thm)],[c529,c530]) ).
cnf(c532,plain,
and(X2,or(and(X,X2),and(X2,X2))) = or(and(X,X2),X2),
inference(transitivity,[status(thm)],[c528,c531]) ).
cnf(c533,plain,
and(X2,or(and(X,X2),neg(neg(X2)))) = or(and(X,X2),X2),
inference(transitivity,[status(thm)],[c125,c532]) ).
cnf(c534,plain,
and(X2,or(and(X,X2),X2)) = or(and(X,X2),X2),
inference(transitivity,[status(thm)],[c116,c533]) ).
cnf(c535,plain,
and(X,or(and(X2,X),X)) = or(and(X2,X),X),
inference(substitution,[status(thm)],[c534]) ).
cnf(c536,plain,
or(and(X2,X),X) = and(X,or(and(X2,X),X)),
inference(symmetry,[status(thm)],[c535]) ).
cnf(c537,plain,
neg(or(and(X2,X),X)) = neg(and(X,or(and(X2,X),X))),
inference(congruence,[status(thm)],[c536]) ).
cnf(c538,plain,
neg(and(X,or(and(X2,X),X))) = f(X,or(and(X2,X),X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c539,plain,
f(X,or(and(X2,X),X)) = or(neg(X),neg(or(and(X2,X),X))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c540,plain,
neg(or(and(X2,X),X)) = and(neg(and(X2,X)),neg(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c541,plain,
or(neg(X),neg(or(and(X2,X),X))) = or(neg(X),and(neg(and(X2,X)),neg(X))),
inference(congruence,[status(thm)],[c540]) ).
cnf(c542,plain,
and(neg(and(X2,X)),neg(X)) = and(f(X2,X),neg(X)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c543,plain,
or(neg(X),and(neg(and(X2,X)),neg(X))) = or(neg(X),and(f(X2,X),neg(X))),
inference(congruence,[status(thm)],[c542]) ).
cnf(c544,plain,
and(f(X2,X),neg(X)) = and(or(neg(X2),neg(X)),neg(X)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c545,plain,
or(neg(X),and(f(X2,X),neg(X))) = or(neg(X),and(or(neg(X2),neg(X)),neg(X))),
inference(congruence,[status(thm)],[c544]) ).
cnf(c546,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c547,plain,
or(X2,X) = or(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c546]) ).
cnf(c548,plain,
and(or(X2,X),X) = and(or(neg(neg(X2)),X),X),
inference(congruence,[status(thm)],[c547]) ).
cnf(c549,plain,
or(and(or(X2,X),X),X) = or(and(or(neg(neg(X2)),X),X),X),
inference(congruence,[status(thm)],[c548]) ).
cnf(c550,plain,
and(or(and(or(X2,X),X),X),X) = and(or(and(or(neg(neg(X2)),X),X),X),X),
inference(congruence,[status(thm)],[c549]) ).
cnf(c551,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c552,plain,
and(or(neg(X2),X),X) = and(or(neg(X2),X),neg(neg(X))),
inference(congruence,[status(thm)],[c551]) ).
cnf(c553,plain,
or(and(or(neg(X2),X),X),X) = or(and(or(neg(X2),X),neg(neg(X))),X),
inference(congruence,[status(thm)],[c552]) ).
cnf(c554,plain,
and(or(and(or(neg(X2),X),X),X),X) = and(or(and(or(neg(X2),X),neg(neg(X))),X),X),
inference(congruence,[status(thm)],[c553]) ).
cnf(c555,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c556,plain,
or(and(or(neg(X2),X),neg(neg(X))),X) = or(and(or(neg(X2),X),neg(neg(X))),neg(neg(X))),
inference(congruence,[status(thm)],[c555]) ).
cnf(c557,plain,
and(or(and(or(neg(X2),X),neg(neg(X))),X),X) = and(or(and(or(neg(X2),X),neg(neg(X))),neg(neg(X))),X),
inference(congruence,[status(thm)],[c556]) ).
cnf(c558,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c559,plain,
and(or(and(or(neg(X2),X),neg(neg(X))),neg(neg(X))),X) = and(or(and(or(neg(X2),X),neg(neg(X))),neg(neg(X))),neg(neg(X))),
inference(congruence,[status(thm)],[c558]) ).
cnf(c560,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c561,plain,
or(neg(X2),X) = or(neg(X2),neg(neg(X))),
inference(congruence,[status(thm)],[c560]) ).
cnf(c562,plain,
and(or(neg(X2),X),neg(neg(X))) = and(or(neg(X2),neg(neg(X))),neg(neg(X))),
inference(congruence,[status(thm)],[c561]) ).
cnf(c563,plain,
or(and(or(neg(X2),X),neg(neg(X))),neg(neg(X))) = or(and(or(neg(X2),neg(neg(X))),neg(neg(X))),neg(neg(X))),
inference(congruence,[status(thm)],[c562]) ).
cnf(c564,plain,
and(or(and(or(neg(X2),X),neg(neg(X))),neg(neg(X))),neg(neg(X))) = and(or(and(or(neg(X2),neg(neg(X))),neg(neg(X))),neg(neg(X))),neg(neg(X))),
inference(congruence,[status(thm)],[c563]) ).
cnf(c565,plain,
or(neg(X2),neg(X)) = f(X2,X),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c566,plain,
and(or(neg(X2),neg(X)),neg(X)) = and(f(X2,X),neg(X)),
inference(congruence,[status(thm)],[c565]) ).
cnf(c567,plain,
or(and(or(neg(X2),neg(X)),neg(X)),neg(X)) = or(and(f(X2,X),neg(X)),neg(X)),
inference(congruence,[status(thm)],[c566]) ).
cnf(c568,plain,
and(or(and(or(neg(X2),neg(X)),neg(X)),neg(X)),neg(X)) = and(or(and(f(X2,X),neg(X)),neg(X)),neg(X)),
inference(congruence,[status(thm)],[c567]) ).
cnf(c569,plain,
f(X2,X) = neg(and(X2,X)),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c570,plain,
and(f(X2,X),neg(X)) = and(neg(and(X2,X)),neg(X)),
inference(congruence,[status(thm)],[c569]) ).
cnf(c571,plain,
or(and(f(X2,X),neg(X)),neg(X)) = or(and(neg(and(X2,X)),neg(X)),neg(X)),
inference(congruence,[status(thm)],[c570]) ).
cnf(c572,plain,
and(or(and(f(X2,X),neg(X)),neg(X)),neg(X)) = and(or(and(neg(and(X2,X)),neg(X)),neg(X)),neg(X)),
inference(congruence,[status(thm)],[c571]) ).
cnf(c573,plain,
neg(or(and(X2,X),X)) = and(neg(and(X2,X)),neg(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c574,plain,
and(neg(and(X2,X)),neg(X)) = neg(or(and(X2,X),X)),
inference(symmetry,[status(thm)],[c573]) ).
cnf(c575,plain,
or(and(neg(and(X2,X)),neg(X)),neg(X)) = or(neg(or(and(X2,X),X)),neg(X)),
inference(congruence,[status(thm)],[c574]) ).
cnf(c576,plain,
and(or(and(neg(and(X2,X)),neg(X)),neg(X)),neg(X)) = and(or(neg(or(and(X2,X),X)),neg(X)),neg(X)),
inference(congruence,[status(thm)],[c575]) ).
cnf(c577,plain,
f(or(and(X2,X),X),X) = or(neg(or(and(X2,X),X)),neg(X)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c578,plain,
or(neg(or(and(X2,X),X)),neg(X)) = f(or(and(X2,X),X),X),
inference(symmetry,[status(thm)],[c577]) ).
cnf(c579,plain,
and(or(neg(or(and(X2,X),X)),neg(X)),neg(X)) = and(f(or(and(X2,X),X),X),neg(X)),
inference(congruence,[status(thm)],[c578]) ).
cnf(c580,plain,
neg(and(or(and(X2,X),X),X)) = f(or(and(X2,X),X),X),
inference(substitution,[status(thm)],[c105]) ).
cnf(c581,plain,
f(or(and(X2,X),X),X) = neg(and(or(and(X2,X),X),X)),
inference(symmetry,[status(thm)],[c580]) ).
cnf(c582,plain,
and(f(or(and(X2,X),X),X),neg(X)) = and(neg(and(or(and(X2,X),X),X)),neg(X)),
inference(congruence,[status(thm)],[c581]) ).
cnf(c583,plain,
neg(or(and(or(and(X2,X),X),X),X)) = and(neg(and(or(and(X2,X),X),X)),neg(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c584,plain,
and(neg(and(or(and(X2,X),X),X)),neg(X)) = neg(or(and(or(and(X2,X),X),X),X)),
inference(symmetry,[status(thm)],[c583]) ).
cnf(c585,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c586,plain,
or(and(X2,X),X) = or(neg(f(X2,X)),X),
inference(congruence,[status(thm)],[c585]) ).
cnf(c587,plain,
and(or(and(X2,X),X),X) = and(or(neg(f(X2,X)),X),X),
inference(congruence,[status(thm)],[c586]) ).
cnf(c588,plain,
or(and(or(and(X2,X),X),X),X) = or(and(or(neg(f(X2,X)),X),X),X),
inference(congruence,[status(thm)],[c587]) ).
cnf(c589,plain,
f(f(X2,X),neg(X)) = or(neg(f(X2,X)),X),
inference(substitution,[status(thm)],[c85]) ).
cnf(c590,plain,
or(neg(f(X2,X)),X) = f(f(X2,X),neg(X)),
inference(symmetry,[status(thm)],[c589]) ).
cnf(c591,plain,
and(or(neg(f(X2,X)),X),X) = and(f(f(X2,X),neg(X)),X),
inference(congruence,[status(thm)],[c590]) ).
cnf(c592,plain,
or(and(or(neg(f(X2,X)),X),X),X) = or(and(f(f(X2,X),neg(X)),X),X),
inference(congruence,[status(thm)],[c591]) ).
cnf(c593,plain,
neg(f(f(f(X2,X),neg(X)),X)) = and(f(f(X2,X),neg(X)),X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c594,plain,
and(f(f(X2,X),neg(X)),X) = neg(f(f(f(X2,X),neg(X)),X)),
inference(symmetry,[status(thm)],[c593]) ).
cnf(c595,plain,
or(and(f(f(X2,X),neg(X)),X),X) = or(neg(f(f(f(X2,X),neg(X)),X)),X),
inference(congruence,[status(thm)],[c594]) ).
cnf(c596,plain,
f(f(f(f(X2,X),neg(X)),X),neg(X)) = or(neg(f(f(f(X2,X),neg(X)),X)),X),
inference(substitution,[status(thm)],[c85]) ).
cnf(c597,plain,
or(neg(f(f(f(X2,X),neg(X)),X)),X) = f(f(f(f(X2,X),neg(X)),X),neg(X)),
inference(symmetry,[status(thm)],[c596]) ).
cnf(c598,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c599,plain,
f(f(X2,X),neg(X)) = f(f(X2,X),f(X,X)),
inference(congruence,[status(thm)],[c598]) ).
cnf(c600,plain,
f(f(f(X2,X),neg(X)),X) = f(f(f(X2,X),f(X,X)),X),
inference(congruence,[status(thm)],[c599]) ).
cnf(c601,plain,
f(f(f(f(X2,X),neg(X)),X),neg(X)) = f(f(f(f(X2,X),f(X,X)),X),neg(X)),
inference(congruence,[status(thm)],[c600]) ).
cnf(c602,plain,
f(f(f(f(X2,X),f(X,X)),X),neg(X)) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c603,plain,
f(f(f(f(X2,X),neg(X)),X),neg(X)) = X,
inference(transitivity,[status(thm)],[c601,c602]) ).
cnf(c604,plain,
or(neg(f(f(f(X2,X),neg(X)),X)),X) = X,
inference(transitivity,[status(thm)],[c597,c603]) ).
cnf(c605,plain,
or(and(f(f(X2,X),neg(X)),X),X) = X,
inference(transitivity,[status(thm)],[c595,c604]) ).
cnf(c606,plain,
or(and(or(neg(f(X2,X)),X),X),X) = X,
inference(transitivity,[status(thm)],[c592,c605]) ).
cnf(c607,plain,
or(and(or(and(X2,X),X),X),X) = X,
inference(transitivity,[status(thm)],[c588,c606]) ).
cnf(c608,plain,
neg(or(and(or(and(X2,X),X),X),X)) = neg(X),
inference(congruence,[status(thm)],[c607]) ).
cnf(c609,plain,
and(neg(and(or(and(X2,X),X),X)),neg(X)) = neg(X),
inference(transitivity,[status(thm)],[c584,c608]) ).
cnf(c610,plain,
and(f(or(and(X2,X),X),X),neg(X)) = neg(X),
inference(transitivity,[status(thm)],[c582,c609]) ).
cnf(c611,plain,
and(or(neg(or(and(X2,X),X)),neg(X)),neg(X)) = neg(X),
inference(transitivity,[status(thm)],[c579,c610]) ).
cnf(c612,plain,
and(or(and(neg(and(X2,X)),neg(X)),neg(X)),neg(X)) = neg(X),
inference(transitivity,[status(thm)],[c576,c611]) ).
cnf(c613,plain,
and(or(and(f(X2,X),neg(X)),neg(X)),neg(X)) = neg(X),
inference(transitivity,[status(thm)],[c572,c612]) ).
cnf(c614,plain,
and(or(and(or(neg(X2),neg(X)),neg(X)),neg(X)),neg(X)) = neg(X),
inference(transitivity,[status(thm)],[c568,c613]) ).
cnf(c615,plain,
and(or(and(or(neg(X2),neg(neg(X))),neg(neg(X))),neg(neg(X))),neg(neg(X))) = neg(neg(X)),
inference(substitution,[status(thm)],[c614]) ).
cnf(c616,plain,
and(or(and(or(neg(X2),neg(neg(X))),neg(neg(X))),neg(neg(X))),neg(neg(X))) = X,
inference(transitivity,[status(thm)],[c615,c79]) ).
cnf(c617,plain,
and(or(and(or(neg(X2),X),neg(neg(X))),neg(neg(X))),neg(neg(X))) = X,
inference(transitivity,[status(thm)],[c564,c616]) ).
cnf(c618,plain,
and(or(and(or(neg(X2),X),neg(neg(X))),neg(neg(X))),X) = X,
inference(transitivity,[status(thm)],[c559,c617]) ).
cnf(c619,plain,
and(or(and(or(neg(X2),X),neg(neg(X))),X),X) = X,
inference(transitivity,[status(thm)],[c557,c618]) ).
cnf(c620,plain,
and(or(and(or(neg(X2),X),X),X),X) = X,
inference(transitivity,[status(thm)],[c554,c619]) ).
cnf(c621,plain,
and(or(and(or(neg(neg(X2)),X),X),X),X) = X,
inference(substitution,[status(thm)],[c620]) ).
cnf(c622,plain,
and(or(and(or(X2,X),X),X),X) = X,
inference(transitivity,[status(thm)],[c550,c621]) ).
cnf(c623,plain,
and(or(and(or(X,X2),X2),X2),X2) = X2,
inference(substitution,[status(thm)],[c622]) ).
cnf(c624,plain,
X2 = and(or(and(or(X,X2),X2),X2),X2),
inference(symmetry,[status(thm)],[c623]) ).
cnf(c625,plain,
or(X2,or(and(or(X,X2),X2),X2)) = or(and(or(and(or(X,X2),X2),X2),X2),or(and(or(X,X2),X2),X2)),
inference(congruence,[status(thm)],[c624]) ).
cnf(c626,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c627,plain,
and(X2,X) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c626]) ).
cnf(c628,plain,
or(and(X2,X),X2) = or(and(X2,neg(neg(X))),X2),
inference(congruence,[status(thm)],[c627]) ).
cnf(c629,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c630,plain,
or(and(X2,neg(X)),X2) = or(and(X2,neg(X)),neg(neg(X2))),
inference(congruence,[status(thm)],[c629]) ).
cnf(c631,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c632,plain,
and(X2,neg(X)) = and(neg(neg(X2)),neg(X)),
inference(congruence,[status(thm)],[c631]) ).
cnf(c633,plain,
or(and(X2,neg(X)),neg(neg(X2))) = or(and(neg(neg(X2)),neg(X)),neg(neg(X2))),
inference(congruence,[status(thm)],[c632]) ).
cnf(c634,plain,
and(neg(X2),neg(X)) = neg(or(X2,X)),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c635,plain,
or(and(neg(X2),neg(X)),neg(X2)) = or(neg(or(X2,X)),neg(X2)),
inference(congruence,[status(thm)],[c634]) ).
cnf(c636,plain,
f(or(X2,X),X2) = or(neg(or(X2,X)),neg(X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c637,plain,
or(neg(or(X2,X)),neg(X2)) = f(or(X2,X),X2),
inference(symmetry,[status(thm)],[c636]) ).
cnf(c638,plain,
neg(and(or(X2,X),X2)) = f(or(X2,X),X2),
inference(substitution,[status(thm)],[c105]) ).
cnf(c639,plain,
f(or(X2,X),X2) = neg(and(or(X2,X),X2)),
inference(symmetry,[status(thm)],[c638]) ).
cnf(c640,plain,
neg(and(or(X2,X),X2)) = neg(X2),
inference(congruence,[status(thm)],[c525]) ).
cnf(c641,plain,
f(or(X2,X),X2) = neg(X2),
inference(transitivity,[status(thm)],[c639,c640]) ).
cnf(c642,plain,
or(neg(or(X2,X)),neg(X2)) = neg(X2),
inference(transitivity,[status(thm)],[c637,c641]) ).
cnf(c643,plain,
or(and(neg(X2),neg(X)),neg(X2)) = neg(X2),
inference(transitivity,[status(thm)],[c635,c642]) ).
cnf(c644,plain,
or(and(neg(neg(X2)),neg(X)),neg(neg(X2))) = neg(neg(X2)),
inference(substitution,[status(thm)],[c643]) ).
cnf(c645,plain,
or(and(neg(neg(X2)),neg(X)),neg(neg(X2))) = X2,
inference(transitivity,[status(thm)],[c644,c79]) ).
cnf(c646,plain,
or(and(X2,neg(X)),neg(neg(X2))) = X2,
inference(transitivity,[status(thm)],[c633,c645]) ).
cnf(c647,plain,
or(and(X2,neg(X)),X2) = X2,
inference(transitivity,[status(thm)],[c630,c646]) ).
cnf(c648,plain,
or(and(X2,neg(neg(X))),X2) = X2,
inference(substitution,[status(thm)],[c647]) ).
cnf(c649,plain,
or(and(X2,X),X2) = X2,
inference(transitivity,[status(thm)],[c628,c648]) ).
cnf(c650,plain,
or(and(or(and(or(X,X2),X2),X2),X2),or(and(or(X,X2),X2),X2)) = or(and(or(X,X2),X2),X2),
inference(substitution,[status(thm)],[c649]) ).
cnf(c651,plain,
or(X2,or(and(or(X,X2),X2),X2)) = or(and(or(X,X2),X2),X2),
inference(transitivity,[status(thm)],[c625,c650]) ).
cnf(c652,plain,
or(X,or(and(or(X2,X),X),X)) = or(and(or(X2,X),X),X),
inference(substitution,[status(thm)],[c651]) ).
cnf(c653,plain,
or(and(or(X2,X),X),X) = or(X,or(and(or(X2,X),X),X)),
inference(symmetry,[status(thm)],[c652]) ).
cnf(c654,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c655,plain,
or(and(X,X2),X2) = or(and(X,X2),neg(neg(X2))),
inference(congruence,[status(thm)],[c654]) ).
cnf(c656,plain,
or(X2,or(and(X,X2),X2)) = or(X2,or(and(X,X2),neg(neg(X2)))),
inference(congruence,[status(thm)],[c655]) ).
cnf(c657,plain,
neg(neg(X)) = and(X,X),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c658,plain,
or(and(X,X2),neg(neg(X2))) = or(and(X,X2),and(X2,X2)),
inference(congruence,[status(thm)],[c657]) ).
cnf(c659,plain,
or(X2,or(and(X,X2),neg(neg(X2)))) = or(X2,or(and(X,X2),and(X2,X2))),
inference(congruence,[status(thm)],[c658]) ).
cnf(c660,plain,
or(or(and(X2,X3),and(X3,X)),and(X3,or(and(X3,or(X2,neg(X2))),neg(X)))) = X3,
inference(substitution,[status(thm)],[c170]) ).
cnf(c661,plain,
X3 = or(or(and(X2,X3),and(X3,X)),and(X3,or(and(X3,or(X2,neg(X2))),neg(X)))),
inference(symmetry,[status(thm)],[c660]) ).
cnf(c662,plain,
or(X3,or(and(X2,X3),and(X3,X))) = or(or(or(and(X2,X3),and(X3,X)),and(X3,or(and(X3,or(X2,neg(X2))),neg(X)))),or(and(X2,X3),and(X3,X))),
inference(congruence,[status(thm)],[c661]) ).
cnf(c663,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c664,plain,
or(X2,X) = or(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c663]) ).
cnf(c665,plain,
or(or(X2,X),X2) = or(or(neg(neg(X2)),X),X2),
inference(congruence,[status(thm)],[c664]) ).
cnf(c666,plain,
and(or(or(X2,X),X2),or(X2,X)) = and(or(or(neg(neg(X2)),X),X2),or(X2,X)),
inference(congruence,[status(thm)],[c665]) ).
cnf(c667,plain,
or(or(X2,X),and(or(or(X2,X),X2),or(X2,X))) = or(or(X2,X),and(or(or(neg(neg(X2)),X),X2),or(X2,X))),
inference(congruence,[status(thm)],[c666]) ).
cnf(c668,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c669,plain,
or(or(neg(neg(X2)),X),X2) = or(or(neg(neg(X2)),X),neg(neg(X2))),
inference(congruence,[status(thm)],[c668]) ).
cnf(c670,plain,
and(or(or(neg(neg(X2)),X),X2),or(X2,X)) = and(or(or(neg(neg(X2)),X),neg(neg(X2))),or(X2,X)),
inference(congruence,[status(thm)],[c669]) ).
cnf(c671,plain,
or(or(X2,X),and(or(or(neg(neg(X2)),X),X2),or(X2,X))) = or(or(X2,X),and(or(or(neg(neg(X2)),X),neg(neg(X2))),or(X2,X))),
inference(congruence,[status(thm)],[c670]) ).
cnf(c672,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c673,plain,
or(X2,X) = or(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c672]) ).
cnf(c674,plain,
and(or(or(neg(neg(X2)),X),neg(neg(X2))),or(X2,X)) = and(or(or(neg(neg(X2)),X),neg(neg(X2))),or(neg(neg(X2)),X)),
inference(congruence,[status(thm)],[c673]) ).
cnf(c675,plain,
or(or(X2,X),and(or(or(neg(neg(X2)),X),neg(neg(X2))),or(X2,X))) = or(or(X2,X),and(or(or(neg(neg(X2)),X),neg(neg(X2))),or(neg(neg(X2)),X))),
inference(congruence,[status(thm)],[c674]) ).
cnf(c676,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c677,plain,
or(X2,X) = or(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c676]) ).
cnf(c678,plain,
or(or(X2,X),and(or(or(neg(neg(X2)),X),neg(neg(X2))),or(neg(neg(X2)),X))) = or(or(neg(neg(X2)),X),and(or(or(neg(neg(X2)),X),neg(neg(X2))),or(neg(neg(X2)),X))),
inference(congruence,[status(thm)],[c677]) ).
cnf(c679,plain,
neg(neg(or(neg(X2),X))) = or(neg(X2),X),
inference(substitution,[status(thm)],[c79]) ).
cnf(c680,plain,
or(neg(X2),X) = neg(neg(or(neg(X2),X))),
inference(symmetry,[status(thm)],[c679]) ).
cnf(c681,plain,
or(or(neg(X2),X),neg(X2)) = or(neg(neg(or(neg(X2),X))),neg(X2)),
inference(congruence,[status(thm)],[c680]) ).
cnf(c682,plain,
and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)) = and(or(neg(neg(or(neg(X2),X))),neg(X2)),or(neg(X2),X)),
inference(congruence,[status(thm)],[c681]) ).
cnf(c683,plain,
or(or(neg(X2),X),and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X))) = or(or(neg(X2),X),and(or(neg(neg(or(neg(X2),X))),neg(X2)),or(neg(X2),X))),
inference(congruence,[status(thm)],[c682]) ).
cnf(c684,plain,
and(or(neg(X2),X),or(neg(X2),X)) = neg(neg(or(neg(X2),X))),
inference(substitution,[status(thm)],[c122]) ).
cnf(c685,plain,
neg(neg(or(neg(X2),X))) = and(or(neg(X2),X),or(neg(X2),X)),
inference(symmetry,[status(thm)],[c684]) ).
cnf(c686,plain,
or(neg(neg(or(neg(X2),X))),neg(X2)) = or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)),
inference(congruence,[status(thm)],[c685]) ).
cnf(c687,plain,
and(or(neg(neg(or(neg(X2),X))),neg(X2)),or(neg(X2),X)) = and(or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)),or(neg(X2),X)),
inference(congruence,[status(thm)],[c686]) ).
cnf(c688,plain,
or(or(neg(X2),X),and(or(neg(neg(or(neg(X2),X))),neg(X2)),or(neg(X2),X))) = or(or(neg(X2),X),and(or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)),or(neg(X2),X))),
inference(congruence,[status(thm)],[c687]) ).
cnf(c689,plain,
neg(neg(or(neg(X2),X))) = or(neg(X2),X),
inference(substitution,[status(thm)],[c79]) ).
cnf(c690,plain,
or(neg(X2),X) = neg(neg(or(neg(X2),X))),
inference(symmetry,[status(thm)],[c689]) ).
cnf(c691,plain,
or(or(neg(X2),X),and(or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)),or(neg(X2),X))) = or(neg(neg(or(neg(X2),X))),and(or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)),or(neg(X2),X))),
inference(congruence,[status(thm)],[c690]) ).
cnf(c692,plain,
and(or(neg(X2),X),or(neg(X2),X)) = neg(neg(or(neg(X2),X))),
inference(substitution,[status(thm)],[c122]) ).
cnf(c693,plain,
neg(neg(or(neg(X2),X))) = and(or(neg(X2),X),or(neg(X2),X)),
inference(symmetry,[status(thm)],[c692]) ).
cnf(c694,plain,
or(neg(neg(or(neg(X2),X))),and(or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)),or(neg(X2),X))) = or(and(or(neg(X2),X),or(neg(X2),X)),and(or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)),or(neg(X2),X))),
inference(congruence,[status(thm)],[c693]) ).
cnf(c695,plain,
neg(f(X3,or(neg(X2),X))) = and(X3,or(neg(X2),X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c696,plain,
and(X3,or(neg(X2),X)) = neg(f(X3,or(neg(X2),X))),
inference(symmetry,[status(thm)],[c695]) ).
cnf(c697,plain,
or(and(X3,or(neg(X2),X)),neg(X2)) = or(neg(f(X3,or(neg(X2),X))),neg(X2)),
inference(congruence,[status(thm)],[c696]) ).
cnf(c698,plain,
and(or(and(X3,or(neg(X2),X)),neg(X2)),or(neg(X2),X)) = and(or(neg(f(X3,or(neg(X2),X))),neg(X2)),or(neg(X2),X)),
inference(congruence,[status(thm)],[c697]) ).
cnf(c699,plain,
or(and(X3,or(neg(X2),X)),and(or(and(X3,or(neg(X2),X)),neg(X2)),or(neg(X2),X))) = or(and(X3,or(neg(X2),X)),and(or(neg(f(X3,or(neg(X2),X))),neg(X2)),or(neg(X2),X))),
inference(congruence,[status(thm)],[c698]) ).
cnf(c700,plain,
f(f(X3,or(neg(X2),X)),X2) = or(neg(f(X3,or(neg(X2),X))),neg(X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c701,plain,
or(neg(f(X3,or(neg(X2),X))),neg(X2)) = f(f(X3,or(neg(X2),X)),X2),
inference(symmetry,[status(thm)],[c700]) ).
cnf(c702,plain,
and(or(neg(f(X3,or(neg(X2),X))),neg(X2)),or(neg(X2),X)) = and(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X)),
inference(congruence,[status(thm)],[c701]) ).
cnf(c703,plain,
or(and(X3,or(neg(X2),X)),and(or(neg(f(X3,or(neg(X2),X))),neg(X2)),or(neg(X2),X))) = or(and(X3,or(neg(X2),X)),and(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X))),
inference(congruence,[status(thm)],[c702]) ).
cnf(c704,plain,
neg(f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X))) = and(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c705,plain,
and(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X)) = neg(f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X))),
inference(symmetry,[status(thm)],[c704]) ).
cnf(c706,plain,
or(and(X3,or(neg(X2),X)),and(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X))) = or(and(X3,or(neg(X2),X)),neg(f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X)))),
inference(congruence,[status(thm)],[c705]) ).
cnf(c707,plain,
neg(f(X3,or(neg(X2),X))) = and(X3,or(neg(X2),X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c708,plain,
and(X3,or(neg(X2),X)) = neg(f(X3,or(neg(X2),X))),
inference(symmetry,[status(thm)],[c707]) ).
cnf(c709,plain,
or(and(X3,or(neg(X2),X)),neg(f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X)))) = or(neg(f(X3,or(neg(X2),X))),neg(f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X)))),
inference(congruence,[status(thm)],[c708]) ).
cnf(c710,plain,
f(f(X3,or(neg(X2),X)),f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X))) = or(neg(f(X3,or(neg(X2),X))),neg(f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c711,plain,
or(neg(f(X3,or(neg(X2),X))),neg(f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X)))) = f(f(X3,or(neg(X2),X)),f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X))),
inference(symmetry,[status(thm)],[c710]) ).
cnf(c712,plain,
X2 = f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c713,plain,
f(f(X3,or(neg(X2),X)),X2) = f(f(X3,or(neg(X2),X)),f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))),
inference(congruence,[status(thm)],[c712]) ).
cnf(c714,plain,
f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X)) = f(f(f(X3,or(neg(X2),X)),f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))),or(neg(X2),X)),
inference(congruence,[status(thm)],[c713]) ).
cnf(c715,plain,
f(f(X3,or(neg(X2),X)),f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X))) = f(f(X3,or(neg(X2),X)),f(f(f(X3,or(neg(X2),X)),f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))),or(neg(X2),X))),
inference(congruence,[status(thm)],[c714]) ).
cnf(c716,plain,
f(f(X3,or(neg(X2),X)),f(f(f(X3,or(neg(X2),X)),f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))),or(neg(X2),X))) = f(f(X3,or(neg(X2),X)),f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c717,plain,
f(f(X3,or(neg(X2),X)),f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))) = or(neg(f(X3,or(neg(X2),X))),neg(f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c718,plain,
neg(f(X3,or(neg(X2),X))) = and(X3,or(neg(X2),X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c719,plain,
or(neg(f(X3,or(neg(X2),X))),neg(f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))))) = or(and(X3,or(neg(X2),X)),neg(f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))))),
inference(congruence,[status(thm)],[c718]) ).
cnf(c720,plain,
neg(f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))) = and(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c721,plain,
or(and(X3,or(neg(X2),X)),neg(f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))))) = or(and(X3,or(neg(X2),X)),and(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))),
inference(congruence,[status(thm)],[c720]) ).
cnf(c722,plain,
or(and(X3,or(neg(X2),X)),and(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))) = or(and(X3,or(neg(X2),X)),neg(X2)),
inference(congruence,[status(thm)],[c217]) ).
cnf(c723,plain,
or(and(X3,or(neg(X2),X)),neg(f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))))) = or(and(X3,or(neg(X2),X)),neg(X2)),
inference(transitivity,[status(thm)],[c721,c722]) ).
cnf(c724,plain,
or(neg(f(X3,or(neg(X2),X))),neg(f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))))) = or(and(X3,or(neg(X2),X)),neg(X2)),
inference(transitivity,[status(thm)],[c719,c723]) ).
cnf(c725,plain,
f(f(X3,or(neg(X2),X)),f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))) = or(and(X3,or(neg(X2),X)),neg(X2)),
inference(transitivity,[status(thm)],[c717,c724]) ).
cnf(c726,plain,
f(f(X3,or(neg(X2),X)),f(f(f(X3,or(neg(X2),X)),f(or(neg(X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))),or(neg(X2),X))) = or(and(X3,or(neg(X2),X)),neg(X2)),
inference(transitivity,[status(thm)],[c716,c725]) ).
cnf(c727,plain,
f(f(X3,or(neg(X2),X)),f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X))) = or(and(X3,or(neg(X2),X)),neg(X2)),
inference(transitivity,[status(thm)],[c715,c726]) ).
cnf(c728,plain,
or(neg(f(X3,or(neg(X2),X))),neg(f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X)))) = or(and(X3,or(neg(X2),X)),neg(X2)),
inference(transitivity,[status(thm)],[c711,c727]) ).
cnf(c729,plain,
or(and(X3,or(neg(X2),X)),neg(f(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X)))) = or(and(X3,or(neg(X2),X)),neg(X2)),
inference(transitivity,[status(thm)],[c709,c728]) ).
cnf(c730,plain,
or(and(X3,or(neg(X2),X)),and(f(f(X3,or(neg(X2),X)),X2),or(neg(X2),X))) = or(and(X3,or(neg(X2),X)),neg(X2)),
inference(transitivity,[status(thm)],[c706,c729]) ).
cnf(c731,plain,
or(and(X3,or(neg(X2),X)),and(or(neg(f(X3,or(neg(X2),X))),neg(X2)),or(neg(X2),X))) = or(and(X3,or(neg(X2),X)),neg(X2)),
inference(transitivity,[status(thm)],[c703,c730]) ).
cnf(c732,plain,
or(and(X3,or(neg(X2),X)),and(or(and(X3,or(neg(X2),X)),neg(X2)),or(neg(X2),X))) = or(and(X3,or(neg(X2),X)),neg(X2)),
inference(transitivity,[status(thm)],[c699,c731]) ).
cnf(c733,plain,
or(and(or(neg(X2),X),or(neg(X2),X)),and(or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)),or(neg(X2),X))) = or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)),
inference(substitution,[status(thm)],[c732]) ).
cnf(c734,plain,
and(or(neg(X2),X),or(neg(X2),X)) = neg(neg(or(neg(X2),X))),
inference(substitution,[status(thm)],[c122]) ).
cnf(c735,plain,
or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)) = or(neg(neg(or(neg(X2),X))),neg(X2)),
inference(congruence,[status(thm)],[c734]) ).
cnf(c736,plain,
neg(neg(or(neg(X2),X))) = or(neg(X2),X),
inference(substitution,[status(thm)],[c79]) ).
cnf(c737,plain,
or(neg(neg(or(neg(X2),X))),neg(X2)) = or(or(neg(X2),X),neg(X2)),
inference(congruence,[status(thm)],[c736]) ).
cnf(c738,plain,
or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)) = or(or(neg(X2),X),neg(X2)),
inference(transitivity,[status(thm)],[c735,c737]) ).
cnf(c739,plain,
or(and(or(neg(X2),X),or(neg(X2),X)),and(or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)),or(neg(X2),X))) = or(or(neg(X2),X),neg(X2)),
inference(transitivity,[status(thm)],[c733,c738]) ).
cnf(c740,plain,
or(neg(neg(or(neg(X2),X))),and(or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)),or(neg(X2),X))) = or(or(neg(X2),X),neg(X2)),
inference(transitivity,[status(thm)],[c694,c739]) ).
cnf(c741,plain,
or(or(neg(X2),X),and(or(and(or(neg(X2),X),or(neg(X2),X)),neg(X2)),or(neg(X2),X))) = or(or(neg(X2),X),neg(X2)),
inference(transitivity,[status(thm)],[c691,c740]) ).
cnf(c742,plain,
or(or(neg(X2),X),and(or(neg(neg(or(neg(X2),X))),neg(X2)),or(neg(X2),X))) = or(or(neg(X2),X),neg(X2)),
inference(transitivity,[status(thm)],[c688,c741]) ).
cnf(c743,plain,
or(or(neg(X2),X),and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X))) = or(or(neg(X2),X),neg(X2)),
inference(transitivity,[status(thm)],[c683,c742]) ).
cnf(c744,plain,
or(or(neg(neg(X2)),X),and(or(or(neg(neg(X2)),X),neg(neg(X2))),or(neg(neg(X2)),X))) = or(or(neg(neg(X2)),X),neg(neg(X2))),
inference(substitution,[status(thm)],[c743]) ).
cnf(c745,plain,
or(neg(neg(X2)),X) = or(X2,X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c746,plain,
or(or(neg(neg(X2)),X),neg(neg(X2))) = or(or(X2,X),neg(neg(X2))),
inference(congruence,[status(thm)],[c745]) ).
cnf(c747,plain,
or(or(X2,X),neg(neg(X2))) = or(or(X2,X),X2),
inference(congruence,[status(thm)],[c79]) ).
cnf(c748,plain,
or(or(neg(neg(X2)),X),neg(neg(X2))) = or(or(X2,X),X2),
inference(transitivity,[status(thm)],[c746,c747]) ).
cnf(c749,plain,
or(or(neg(neg(X2)),X),and(or(or(neg(neg(X2)),X),neg(neg(X2))),or(neg(neg(X2)),X))) = or(or(X2,X),X2),
inference(transitivity,[status(thm)],[c744,c748]) ).
cnf(c750,plain,
or(or(X2,X),and(or(or(neg(neg(X2)),X),neg(neg(X2))),or(neg(neg(X2)),X))) = or(or(X2,X),X2),
inference(transitivity,[status(thm)],[c678,c749]) ).
cnf(c751,plain,
or(or(X2,X),and(or(or(neg(neg(X2)),X),neg(neg(X2))),or(X2,X))) = or(or(X2,X),X2),
inference(transitivity,[status(thm)],[c675,c750]) ).
cnf(c752,plain,
or(or(X2,X),and(or(or(neg(neg(X2)),X),X2),or(X2,X))) = or(or(X2,X),X2),
inference(transitivity,[status(thm)],[c671,c751]) ).
cnf(c753,plain,
or(or(X2,X),and(or(or(X2,X),X2),or(X2,X))) = or(or(X2,X),X2),
inference(transitivity,[status(thm)],[c667,c752]) ).
cnf(c754,plain,
or(or(X2,X),X2) = or(or(X2,X),and(or(or(X2,X),X2),or(X2,X))),
inference(symmetry,[status(thm)],[c753]) ).
cnf(c755,plain,
and(or(or(X2,X),X2),or(X2,X)) = or(X2,X),
inference(substitution,[status(thm)],[c525]) ).
cnf(c756,plain,
or(or(X2,X),and(or(or(X2,X),X2),or(X2,X))) = or(or(X2,X),or(X2,X)),
inference(congruence,[status(thm)],[c755]) ).
cnf(c757,plain,
or(or(X2,X),or(X2,X)) = neg(neg(or(X2,X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c758,plain,
neg(neg(or(X2,X))) = or(X2,X),
inference(substitution,[status(thm)],[c79]) ).
cnf(c759,plain,
or(or(X2,X),or(X2,X)) = or(X2,X),
inference(transitivity,[status(thm)],[c757,c758]) ).
cnf(c760,plain,
or(or(X2,X),and(or(or(X2,X),X2),or(X2,X))) = or(X2,X),
inference(transitivity,[status(thm)],[c756,c759]) ).
cnf(c761,plain,
or(or(X2,X),X2) = or(X2,X),
inference(transitivity,[status(thm)],[c754,c760]) ).
cnf(c762,plain,
or(or(or(and(X2,X3),and(X3,X)),and(X3,or(and(X3,or(X2,neg(X2))),neg(X)))),or(and(X2,X3),and(X3,X))) = or(or(and(X2,X3),and(X3,X)),and(X3,or(and(X3,or(X2,neg(X2))),neg(X)))),
inference(substitution,[status(thm)],[c761]) ).
cnf(c763,plain,
or(or(and(X2,X3),and(X3,X)),and(X3,or(and(X3,or(X2,neg(X2))),neg(X)))) = X3,
inference(substitution,[status(thm)],[c170]) ).
cnf(c764,plain,
or(or(or(and(X2,X3),and(X3,X)),and(X3,or(and(X3,or(X2,neg(X2))),neg(X)))),or(and(X2,X3),and(X3,X))) = X3,
inference(transitivity,[status(thm)],[c762,c763]) ).
cnf(c765,plain,
or(X3,or(and(X2,X3),and(X3,X))) = X3,
inference(transitivity,[status(thm)],[c662,c764]) ).
cnf(c766,plain,
or(X2,or(and(X,X2),and(X2,X2))) = X2,
inference(substitution,[status(thm)],[c765]) ).
cnf(c767,plain,
or(X2,or(and(X,X2),neg(neg(X2)))) = X2,
inference(transitivity,[status(thm)],[c659,c766]) ).
cnf(c768,plain,
or(X2,or(and(X,X2),X2)) = X2,
inference(transitivity,[status(thm)],[c656,c767]) ).
cnf(c769,plain,
or(X,or(and(or(X2,X),X),X)) = X,
inference(substitution,[status(thm)],[c768]) ).
cnf(c770,plain,
or(and(or(X2,X),X),X) = X,
inference(transitivity,[status(thm)],[c653,c769]) ).
cnf(c771,plain,
or(and(or(X,X2),X2),X2) = X2,
inference(substitution,[status(thm)],[c770]) ).
cnf(c772,plain,
X2 = or(and(or(X,X2),X2),X2),
inference(symmetry,[status(thm)],[c771]) ).
cnf(c773,plain,
or(X2,and(or(X,X2),X2)) = or(or(and(or(X,X2),X2),X2),and(or(X,X2),X2)),
inference(congruence,[status(thm)],[c772]) ).
cnf(c774,plain,
or(or(and(or(X,X2),X2),X2),and(or(X,X2),X2)) = or(and(or(X,X2),X2),X2),
inference(substitution,[status(thm)],[c761]) ).
cnf(c775,plain,
or(and(or(X,X2),X2),X2) = X2,
inference(substitution,[status(thm)],[c770]) ).
cnf(c776,plain,
or(or(and(or(X,X2),X2),X2),and(or(X,X2),X2)) = X2,
inference(transitivity,[status(thm)],[c774,c775]) ).
cnf(c777,plain,
or(X2,and(or(X,X2),X2)) = X2,
inference(transitivity,[status(thm)],[c773,c776]) ).
cnf(c778,plain,
or(neg(X),and(or(neg(X2),neg(X)),neg(X))) = neg(X),
inference(substitution,[status(thm)],[c777]) ).
cnf(c779,plain,
or(neg(X),and(f(X2,X),neg(X))) = neg(X),
inference(transitivity,[status(thm)],[c545,c778]) ).
cnf(c780,plain,
or(neg(X),and(neg(and(X2,X)),neg(X))) = neg(X),
inference(transitivity,[status(thm)],[c543,c779]) ).
cnf(c781,plain,
or(neg(X),neg(or(and(X2,X),X))) = neg(X),
inference(transitivity,[status(thm)],[c541,c780]) ).
cnf(c782,plain,
f(X,or(and(X2,X),X)) = neg(X),
inference(transitivity,[status(thm)],[c539,c781]) ).
cnf(c783,plain,
neg(and(X,or(and(X2,X),X))) = neg(X),
inference(transitivity,[status(thm)],[c538,c782]) ).
cnf(c784,plain,
neg(or(and(X2,X),X)) = neg(X),
inference(transitivity,[status(thm)],[c537,c783]) ).
cnf(c785,plain,
and(neg(and(X2,X)),neg(X)) = neg(X),
inference(transitivity,[status(thm)],[c113,c784]) ).
cnf(c786,plain,
and(f(X2,X),neg(X)) = neg(X),
inference(transitivity,[status(thm)],[c107,c785]) ).
cnf(c787,plain,
and(or(neg(X2),neg(X)),neg(X)) = neg(X),
inference(transitivity,[status(thm)],[c101,c786]) ).
cnf(c788,plain,
and(or(neg(X2),neg(neg(X))),neg(neg(X))) = neg(neg(X)),
inference(substitution,[status(thm)],[c787]) ).
cnf(c789,plain,
and(or(neg(X2),neg(neg(X))),neg(neg(X))) = X,
inference(transitivity,[status(thm)],[c788,c79]) ).
cnf(c790,plain,
and(or(neg(X2),X),neg(neg(X))) = X,
inference(transitivity,[status(thm)],[c99,c789]) ).
cnf(c791,plain,
and(or(neg(X2),X),X) = X,
inference(transitivity,[status(thm)],[c96,c790]) ).
cnf(c792,plain,
and(or(neg(neg(X2)),X),X) = X,
inference(substitution,[status(thm)],[c791]) ).
cnf(c793,plain,
and(or(X2,X),X) = X,
inference(transitivity,[status(thm)],[c94,c792]) ).
cnf(c794,plain,
and(or(X,X2),X2) = X2,
inference(substitution,[status(thm)],[c793]) ).
cnf(c795,plain,
X2 = and(or(X,X2),X2),
inference(symmetry,[status(thm)],[c794]) ).
cnf(c796,plain,
and(X2,or(X,X2)) = and(and(or(X,X2),X2),or(X,X2)),
inference(congruence,[status(thm)],[c795]) ).
cnf(c797,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c798,plain,
and(X2,X) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c797]) ).
cnf(c799,plain,
and(and(X2,X),X2) = and(and(X2,neg(neg(X))),X2),
inference(congruence,[status(thm)],[c798]) ).
cnf(c800,plain,
or(and(and(X2,X),X2),and(X2,X)) = or(and(and(X2,neg(neg(X))),X2),and(X2,X)),
inference(congruence,[status(thm)],[c799]) ).
cnf(c801,plain,
and(and(X2,X),or(and(and(X2,X),X2),and(X2,X))) = and(and(X2,X),or(and(and(X2,neg(neg(X))),X2),and(X2,X))),
inference(congruence,[status(thm)],[c800]) ).
cnf(c802,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c803,plain,
and(X2,X) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c802]) ).
cnf(c804,plain,
or(and(and(X2,neg(neg(X))),X2),and(X2,X)) = or(and(and(X2,neg(neg(X))),X2),and(X2,neg(neg(X)))),
inference(congruence,[status(thm)],[c803]) ).
cnf(c805,plain,
and(and(X2,X),or(and(and(X2,neg(neg(X))),X2),and(X2,X))) = and(and(X2,X),or(and(and(X2,neg(neg(X))),X2),and(X2,neg(neg(X))))),
inference(congruence,[status(thm)],[c804]) ).
cnf(c806,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c807,plain,
and(X2,X) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c806]) ).
cnf(c808,plain,
and(and(X2,X),or(and(and(X2,neg(neg(X))),X2),and(X2,neg(neg(X))))) = and(and(X2,neg(neg(X))),or(and(and(X2,neg(neg(X))),X2),and(X2,neg(neg(X))))),
inference(congruence,[status(thm)],[c807]) ).
cnf(c809,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c810,plain,
and(X2,neg(X)) = and(neg(neg(X2)),neg(X)),
inference(congruence,[status(thm)],[c809]) ).
cnf(c811,plain,
and(and(X2,neg(X)),X2) = and(and(neg(neg(X2)),neg(X)),X2),
inference(congruence,[status(thm)],[c810]) ).
cnf(c812,plain,
or(and(and(X2,neg(X)),X2),and(X2,neg(X))) = or(and(and(neg(neg(X2)),neg(X)),X2),and(X2,neg(X))),
inference(congruence,[status(thm)],[c811]) ).
cnf(c813,plain,
and(and(X2,neg(X)),or(and(and(X2,neg(X)),X2),and(X2,neg(X)))) = and(and(X2,neg(X)),or(and(and(neg(neg(X2)),neg(X)),X2),and(X2,neg(X)))),
inference(congruence,[status(thm)],[c812]) ).
cnf(c814,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c815,plain,
and(and(neg(neg(X2)),neg(X)),X2) = and(and(neg(neg(X2)),neg(X)),neg(neg(X2))),
inference(congruence,[status(thm)],[c814]) ).
cnf(c816,plain,
or(and(and(neg(neg(X2)),neg(X)),X2),and(X2,neg(X))) = or(and(and(neg(neg(X2)),neg(X)),neg(neg(X2))),and(X2,neg(X))),
inference(congruence,[status(thm)],[c815]) ).
cnf(c817,plain,
and(and(X2,neg(X)),or(and(and(neg(neg(X2)),neg(X)),X2),and(X2,neg(X)))) = and(and(X2,neg(X)),or(and(and(neg(neg(X2)),neg(X)),neg(neg(X2))),and(X2,neg(X)))),
inference(congruence,[status(thm)],[c816]) ).
cnf(c818,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c819,plain,
and(X2,neg(X)) = and(neg(neg(X2)),neg(X)),
inference(congruence,[status(thm)],[c818]) ).
cnf(c820,plain,
or(and(and(neg(neg(X2)),neg(X)),neg(neg(X2))),and(X2,neg(X))) = or(and(and(neg(neg(X2)),neg(X)),neg(neg(X2))),and(neg(neg(X2)),neg(X))),
inference(congruence,[status(thm)],[c819]) ).
cnf(c821,plain,
and(and(X2,neg(X)),or(and(and(neg(neg(X2)),neg(X)),neg(neg(X2))),and(X2,neg(X)))) = and(and(X2,neg(X)),or(and(and(neg(neg(X2)),neg(X)),neg(neg(X2))),and(neg(neg(X2)),neg(X)))),
inference(congruence,[status(thm)],[c820]) ).
cnf(c822,plain,
neg(or(neg(X2),X)) = and(neg(neg(X2)),neg(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c823,plain,
and(neg(neg(X2)),neg(X)) = neg(or(neg(X2),X)),
inference(symmetry,[status(thm)],[c822]) ).
cnf(c824,plain,
and(and(neg(neg(X2)),neg(X)),neg(neg(X2))) = and(neg(or(neg(X2),X)),neg(neg(X2))),
inference(congruence,[status(thm)],[c823]) ).
cnf(c825,plain,
or(and(and(neg(neg(X2)),neg(X)),neg(neg(X2))),and(neg(neg(X2)),neg(X))) = or(and(neg(or(neg(X2),X)),neg(neg(X2))),and(neg(neg(X2)),neg(X))),
inference(congruence,[status(thm)],[c824]) ).
cnf(c826,plain,
and(and(X2,neg(X)),or(and(and(neg(neg(X2)),neg(X)),neg(neg(X2))),and(neg(neg(X2)),neg(X)))) = and(and(X2,neg(X)),or(and(neg(or(neg(X2),X)),neg(neg(X2))),and(neg(neg(X2)),neg(X)))),
inference(congruence,[status(thm)],[c825]) ).
cnf(c827,plain,
neg(or(neg(X2),X)) = and(neg(neg(X2)),neg(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c828,plain,
and(neg(neg(X2)),neg(X)) = neg(or(neg(X2),X)),
inference(symmetry,[status(thm)],[c827]) ).
cnf(c829,plain,
or(and(neg(or(neg(X2),X)),neg(neg(X2))),and(neg(neg(X2)),neg(X))) = or(and(neg(or(neg(X2),X)),neg(neg(X2))),neg(or(neg(X2),X))),
inference(congruence,[status(thm)],[c828]) ).
cnf(c830,plain,
and(and(X2,neg(X)),or(and(neg(or(neg(X2),X)),neg(neg(X2))),and(neg(neg(X2)),neg(X)))) = and(and(X2,neg(X)),or(and(neg(or(neg(X2),X)),neg(neg(X2))),neg(or(neg(X2),X)))),
inference(congruence,[status(thm)],[c829]) ).
cnf(c831,plain,
neg(or(or(neg(X2),X),neg(X2))) = and(neg(or(neg(X2),X)),neg(neg(X2))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c832,plain,
and(neg(or(neg(X2),X)),neg(neg(X2))) = neg(or(or(neg(X2),X),neg(X2))),
inference(symmetry,[status(thm)],[c831]) ).
cnf(c833,plain,
or(and(neg(or(neg(X2),X)),neg(neg(X2))),neg(or(neg(X2),X))) = or(neg(or(or(neg(X2),X),neg(X2))),neg(or(neg(X2),X))),
inference(congruence,[status(thm)],[c832]) ).
cnf(c834,plain,
and(and(X2,neg(X)),or(and(neg(or(neg(X2),X)),neg(neg(X2))),neg(or(neg(X2),X)))) = and(and(X2,neg(X)),or(neg(or(or(neg(X2),X),neg(X2))),neg(or(neg(X2),X)))),
inference(congruence,[status(thm)],[c833]) ).
cnf(c835,plain,
f(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)) = or(neg(or(or(neg(X2),X),neg(X2))),neg(or(neg(X2),X))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c836,plain,
or(neg(or(or(neg(X2),X),neg(X2))),neg(or(neg(X2),X))) = f(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)),
inference(symmetry,[status(thm)],[c835]) ).
cnf(c837,plain,
and(and(X2,neg(X)),or(neg(or(or(neg(X2),X),neg(X2))),neg(or(neg(X2),X)))) = and(and(X2,neg(X)),f(or(or(neg(X2),X),neg(X2)),or(neg(X2),X))),
inference(congruence,[status(thm)],[c836]) ).
cnf(c838,plain,
neg(and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X))) = f(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c839,plain,
f(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)) = neg(and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X))),
inference(symmetry,[status(thm)],[c838]) ).
cnf(c840,plain,
and(and(X2,neg(X)),f(or(or(neg(X2),X),neg(X2)),or(neg(X2),X))) = and(and(X2,neg(X)),neg(and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))),
inference(congruence,[status(thm)],[c839]) ).
cnf(c841,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c842,plain,
and(X2,neg(X)) = and(neg(neg(X2)),neg(X)),
inference(congruence,[status(thm)],[c841]) ).
cnf(c843,plain,
and(and(X2,neg(X)),neg(and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))) = and(and(neg(neg(X2)),neg(X)),neg(and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))),
inference(congruence,[status(thm)],[c842]) ).
cnf(c844,plain,
neg(or(neg(X2),X)) = and(neg(neg(X2)),neg(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c845,plain,
and(neg(neg(X2)),neg(X)) = neg(or(neg(X2),X)),
inference(symmetry,[status(thm)],[c844]) ).
cnf(c846,plain,
and(and(neg(neg(X2)),neg(X)),neg(and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))) = and(neg(or(neg(X2),X)),neg(and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))),
inference(congruence,[status(thm)],[c845]) ).
cnf(c847,plain,
neg(or(or(neg(X2),X),and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))) = and(neg(or(neg(X2),X)),neg(and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c848,plain,
and(neg(or(neg(X2),X)),neg(and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))) = neg(or(or(neg(X2),X),and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))),
inference(symmetry,[status(thm)],[c847]) ).
cnf(c849,plain,
neg(or(or(neg(X2),X),and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))) = neg(or(or(neg(X2),X),neg(X2))),
inference(congruence,[status(thm)],[c743]) ).
cnf(c850,plain,
neg(or(or(neg(X2),X),neg(X2))) = and(neg(or(neg(X2),X)),neg(neg(X2))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c851,plain,
neg(or(neg(X2),X)) = and(neg(neg(X2)),neg(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c852,plain,
and(neg(or(neg(X2),X)),neg(neg(X2))) = and(and(neg(neg(X2)),neg(X)),neg(neg(X2))),
inference(congruence,[status(thm)],[c851]) ).
cnf(c853,plain,
and(neg(neg(X2)),neg(X)) = and(X2,neg(X)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c854,plain,
and(and(neg(neg(X2)),neg(X)),neg(neg(X2))) = and(and(X2,neg(X)),neg(neg(X2))),
inference(congruence,[status(thm)],[c853]) ).
cnf(c855,plain,
and(and(X2,neg(X)),neg(neg(X2))) = and(and(X2,neg(X)),X2),
inference(congruence,[status(thm)],[c79]) ).
cnf(c856,plain,
and(and(neg(neg(X2)),neg(X)),neg(neg(X2))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c854,c855]) ).
cnf(c857,plain,
and(neg(or(neg(X2),X)),neg(neg(X2))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c852,c856]) ).
cnf(c858,plain,
neg(or(or(neg(X2),X),neg(X2))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c850,c857]) ).
cnf(c859,plain,
neg(or(or(neg(X2),X),and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c849,c858]) ).
cnf(c860,plain,
and(neg(or(neg(X2),X)),neg(and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c848,c859]) ).
cnf(c861,plain,
and(and(neg(neg(X2)),neg(X)),neg(and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c846,c860]) ).
cnf(c862,plain,
and(and(X2,neg(X)),neg(and(or(or(neg(X2),X),neg(X2)),or(neg(X2),X)))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c843,c861]) ).
cnf(c863,plain,
and(and(X2,neg(X)),f(or(or(neg(X2),X),neg(X2)),or(neg(X2),X))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c840,c862]) ).
cnf(c864,plain,
and(and(X2,neg(X)),or(neg(or(or(neg(X2),X),neg(X2))),neg(or(neg(X2),X)))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c837,c863]) ).
cnf(c865,plain,
and(and(X2,neg(X)),or(and(neg(or(neg(X2),X)),neg(neg(X2))),neg(or(neg(X2),X)))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c834,c864]) ).
cnf(c866,plain,
and(and(X2,neg(X)),or(and(neg(or(neg(X2),X)),neg(neg(X2))),and(neg(neg(X2)),neg(X)))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c830,c865]) ).
cnf(c867,plain,
and(and(X2,neg(X)),or(and(and(neg(neg(X2)),neg(X)),neg(neg(X2))),and(neg(neg(X2)),neg(X)))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c826,c866]) ).
cnf(c868,plain,
and(and(X2,neg(X)),or(and(and(neg(neg(X2)),neg(X)),neg(neg(X2))),and(X2,neg(X)))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c821,c867]) ).
cnf(c869,plain,
and(and(X2,neg(X)),or(and(and(neg(neg(X2)),neg(X)),X2),and(X2,neg(X)))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c817,c868]) ).
cnf(c870,plain,
and(and(X2,neg(X)),or(and(and(X2,neg(X)),X2),and(X2,neg(X)))) = and(and(X2,neg(X)),X2),
inference(transitivity,[status(thm)],[c813,c869]) ).
cnf(c871,plain,
and(and(X2,neg(neg(X))),or(and(and(X2,neg(neg(X))),X2),and(X2,neg(neg(X))))) = and(and(X2,neg(neg(X))),X2),
inference(substitution,[status(thm)],[c870]) ).
cnf(c872,plain,
and(X2,neg(neg(X))) = and(X2,X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c873,plain,
and(and(X2,neg(neg(X))),X2) = and(and(X2,X),X2),
inference(congruence,[status(thm)],[c872]) ).
cnf(c874,plain,
and(and(X2,neg(neg(X))),or(and(and(X2,neg(neg(X))),X2),and(X2,neg(neg(X))))) = and(and(X2,X),X2),
inference(transitivity,[status(thm)],[c871,c873]) ).
cnf(c875,plain,
and(and(X2,X),or(and(and(X2,neg(neg(X))),X2),and(X2,neg(neg(X))))) = and(and(X2,X),X2),
inference(transitivity,[status(thm)],[c808,c874]) ).
cnf(c876,plain,
and(and(X2,X),or(and(and(X2,neg(neg(X))),X2),and(X2,X))) = and(and(X2,X),X2),
inference(transitivity,[status(thm)],[c805,c875]) ).
cnf(c877,plain,
and(and(X2,X),or(and(and(X2,X),X2),and(X2,X))) = and(and(X2,X),X2),
inference(transitivity,[status(thm)],[c801,c876]) ).
cnf(c878,plain,
and(and(X2,X),X2) = and(and(X2,X),or(and(and(X2,X),X2),and(X2,X))),
inference(symmetry,[status(thm)],[c877]) ).
cnf(c879,plain,
or(and(and(X2,X),X2),and(X2,X)) = and(X2,X),
inference(substitution,[status(thm)],[c649]) ).
cnf(c880,plain,
and(and(X2,X),or(and(and(X2,X),X2),and(X2,X))) = and(and(X2,X),and(X2,X)),
inference(congruence,[status(thm)],[c879]) ).
cnf(c881,plain,
and(and(X2,X),and(X2,X)) = neg(neg(and(X2,X))),
inference(substitution,[status(thm)],[c122]) ).
cnf(c882,plain,
neg(neg(and(X2,X))) = and(X2,X),
inference(substitution,[status(thm)],[c79]) ).
cnf(c883,plain,
and(and(X2,X),and(X2,X)) = and(X2,X),
inference(transitivity,[status(thm)],[c881,c882]) ).
cnf(c884,plain,
and(and(X2,X),or(and(and(X2,X),X2),and(X2,X))) = and(X2,X),
inference(transitivity,[status(thm)],[c880,c883]) ).
cnf(c885,plain,
and(and(X2,X),X2) = and(X2,X),
inference(transitivity,[status(thm)],[c878,c884]) ).
cnf(c886,plain,
and(and(or(X,X2),X2),or(X,X2)) = and(or(X,X2),X2),
inference(substitution,[status(thm)],[c885]) ).
cnf(c887,plain,
and(or(X,X2),X2) = X2,
inference(substitution,[status(thm)],[c793]) ).
cnf(c888,plain,
and(and(or(X,X2),X2),or(X,X2)) = X2,
inference(transitivity,[status(thm)],[c886,c887]) ).
cnf(c889,plain,
and(X2,or(X,X2)) = X2,
inference(transitivity,[status(thm)],[c796,c888]) ).
cnf(c890,plain,
and(X,or(X2,X)) = X,
inference(substitution,[status(thm)],[c889]) ).
cnf(c891,plain,
X = and(X,or(X2,X)),
inference(symmetry,[status(thm)],[c890]) ).
cnf(c892,plain,
or(X,X2) = or(and(X,or(X2,X)),X2),
inference(congruence,[status(thm)],[c891]) ).
cnf(c893,plain,
or(or(X2,X),or(X,X2)) = or(or(X2,X),or(and(X,or(X2,X)),X2)),
inference(congruence,[status(thm)],[c892]) ).
cnf(c894,plain,
X2 = and(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X))))),
inference(symmetry,[status(thm)],[c358]) ).
cnf(c895,plain,
or(and(X,or(X3,X2)),X3) = or(and(X,or(X3,X2)),and(or(X3,X2),or(X3,and(or(X3,X2),and(neg(X3),neg(X2)))))),
inference(congruence,[status(thm)],[c894]) ).
cnf(c896,plain,
or(or(X3,X2),or(and(X,or(X3,X2)),X3)) = or(or(X3,X2),or(and(X,or(X3,X2)),and(or(X3,X2),or(X3,and(or(X3,X2),and(neg(X3),neg(X2))))))),
inference(congruence,[status(thm)],[c895]) ).
cnf(c897,plain,
or(or(X3,X2),or(and(X,or(X3,X2)),and(or(X3,X2),or(X3,and(or(X3,X2),and(neg(X3),neg(X2))))))) = or(X3,X2),
inference(substitution,[status(thm)],[c765]) ).
cnf(c898,plain,
or(or(X3,X2),or(and(X,or(X3,X2)),X3)) = or(X3,X2),
inference(transitivity,[status(thm)],[c896,c897]) ).
cnf(c899,plain,
or(or(X2,X),or(and(X,or(X2,X)),X2)) = or(X2,X),
inference(substitution,[status(thm)],[c898]) ).
cnf(c900,plain,
or(or(X2,X),or(X,X2)) = or(X2,X),
inference(transitivity,[status(thm)],[c893,c899]) ).
cnf(c901,plain,
or(or(X,X2),or(X2,X)) = or(X,X2),
inference(substitution,[status(thm)],[c900]) ).
cnf(c902,plain,
or(X,X2) = or(or(X,X2),or(X2,X)),
inference(symmetry,[status(thm)],[c901]) ).
cnf(c903,plain,
or(X2,X) = or(or(X2,X),or(X,X2)),
inference(symmetry,[status(thm)],[c900]) ).
cnf(c904,plain,
or(or(X,X2),or(X2,X)) = or(or(X,X2),or(or(X2,X),or(X,X2))),
inference(congruence,[status(thm)],[c903]) ).
cnf(c905,plain,
and(or(X,X2),X2) = X2,
inference(substitution,[status(thm)],[c793]) ).
cnf(c906,plain,
X2 = and(or(X,X2),X2),
inference(symmetry,[status(thm)],[c905]) ).
cnf(c907,plain,
or(X2,or(X,X2)) = or(and(or(X,X2),X2),or(X,X2)),
inference(congruence,[status(thm)],[c906]) ).
cnf(c908,plain,
or(and(or(X,X2),X2),or(X,X2)) = or(X,X2),
inference(substitution,[status(thm)],[c649]) ).
cnf(c909,plain,
or(X2,or(X,X2)) = or(X,X2),
inference(transitivity,[status(thm)],[c907,c908]) ).
cnf(c910,plain,
or(or(X,X2),or(or(X2,X),or(X,X2))) = or(or(X2,X),or(X,X2)),
inference(substitution,[status(thm)],[c909]) ).
cnf(c911,plain,
or(or(X,X2),or(or(X2,X),or(X,X2))) = or(X2,X),
inference(transitivity,[status(thm)],[c910,c900]) ).
cnf(c912,plain,
or(or(X,X2),or(X2,X)) = or(X2,X),
inference(transitivity,[status(thm)],[c904,c911]) ).
cnf(c913,plain,
or(X,X2) = or(X2,X),
inference(transitivity,[status(thm)],[c902,c912]) ).
cnf(c914,plain,
or(X2,X) = or(X,X2),
inference(substitution,[status(thm)],[c913]) ).
cnf(c915,plain,
or(X2,or(X3,X)) = or(X2,or(X,X3)),
inference(congruence,[status(thm)],[c914]) ).
cnf(c916,plain,
or(X2,or(X,X3)) = or(or(X,X3),X2),
inference(substitution,[status(thm)],[c913]) ).
cnf(c917,plain,
or(and(X3,X2),or(X,X3)) = or(or(X,X3),and(X3,X2)),
inference(substitution,[status(thm)],[c913]) ).
cnf(c918,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c919,plain,
and(X,X2) = and(neg(neg(X)),X2),
inference(congruence,[status(thm)],[c918]) ).
cnf(c920,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c921,plain,
and(neg(X2),X) = and(neg(X2),neg(neg(X))),
inference(congruence,[status(thm)],[c920]) ).
cnf(c922,plain,
neg(or(X,X2)) = and(neg(X),neg(X2)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c923,plain,
and(neg(X),neg(X2)) = neg(or(X,X2)),
inference(symmetry,[status(thm)],[c922]) ).
cnf(c924,plain,
neg(or(X,X2)) = neg(or(X2,X)),
inference(congruence,[status(thm)],[c913]) ).
cnf(c925,plain,
neg(or(X,X2)) = and(neg(X2),neg(X)),
inference(transitivity,[status(thm)],[c924,c111]) ).
cnf(c926,plain,
and(neg(X),neg(X2)) = and(neg(X2),neg(X)),
inference(transitivity,[status(thm)],[c923,c925]) ).
cnf(c927,plain,
and(neg(X2),neg(neg(X))) = and(neg(neg(X)),neg(X2)),
inference(substitution,[status(thm)],[c926]) ).
cnf(c928,plain,
and(neg(neg(X)),neg(X2)) = and(X,neg(X2)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c929,plain,
and(neg(X2),neg(neg(X))) = and(X,neg(X2)),
inference(transitivity,[status(thm)],[c927,c928]) ).
cnf(c930,plain,
and(neg(X2),X) = and(X,neg(X2)),
inference(transitivity,[status(thm)],[c921,c929]) ).
cnf(c931,plain,
and(neg(neg(X)),X2) = and(X2,neg(neg(X))),
inference(substitution,[status(thm)],[c930]) ).
cnf(c932,plain,
and(X2,neg(neg(X))) = and(X2,X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c933,plain,
and(neg(neg(X)),X2) = and(X2,X),
inference(transitivity,[status(thm)],[c931,c932]) ).
cnf(c934,plain,
and(X,X2) = and(X2,X),
inference(transitivity,[status(thm)],[c919,c933]) ).
cnf(c935,plain,
and(X2,X) = and(X,X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c936,plain,
or(or(X3,X2),and(X2,X)) = or(or(X3,X2),and(X,X2)),
inference(congruence,[status(thm)],[c935]) ).
cnf(c937,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c938,plain,
and(X,X2) = and(X,neg(neg(X2))),
inference(congruence,[status(thm)],[c937]) ).
cnf(c939,plain,
or(or(X3,X2),and(X,X2)) = or(or(X3,X2),and(X,neg(neg(X2)))),
inference(congruence,[status(thm)],[c938]) ).
cnf(c940,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c941,plain,
or(X2,X) = or(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c940]) ).
cnf(c942,plain,
or(or(X3,X2),and(X,neg(neg(X2)))) = or(or(X3,neg(neg(X2))),and(X,neg(neg(X2)))),
inference(congruence,[status(thm)],[c941]) ).
cnf(c943,plain,
or(X2,neg(X)) = or(neg(X),X2),
inference(substitution,[status(thm)],[c913]) ).
cnf(c944,plain,
or(or(X3,neg(X2)),and(X,neg(X2))) = or(or(neg(X2),X3),and(X,neg(X2))),
inference(congruence,[status(thm)],[c943]) ).
cnf(c945,plain,
and(neg(X),X) = and(X,neg(X)),
inference(substitution,[status(thm)],[c930]) ).
cnf(c946,plain,
and(X,neg(X)) = and(neg(X),X),
inference(symmetry,[status(thm)],[c945]) ).
cnf(c947,plain,
or(and(neg(X2),X),and(X2,neg(X2))) = or(and(neg(X2),X),and(neg(X2),X2)),
inference(congruence,[status(thm)],[c946]) ).
cnf(c948,plain,
and(or(and(neg(X3),X2),and(X3,neg(X3))),X) = and(or(and(neg(X3),X2),and(neg(X3),X3)),X),
inference(congruence,[status(thm)],[c947]) ).
cnf(c949,plain,
or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(X3,neg(X3))),X)) = or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(neg(X3),X3)),X)),
inference(congruence,[status(thm)],[c948]) ).
cnf(c950,plain,
and(neg(X3),or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(X3,neg(X3))),X))) = and(neg(X3),or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(neg(X3),X3)),X))),
inference(congruence,[status(thm)],[c949]) ).
cnf(c951,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c952,plain,
and(neg(X),X) = and(neg(X),neg(neg(X))),
inference(congruence,[status(thm)],[c951]) ).
cnf(c953,plain,
or(and(neg(X2),X),and(neg(X2),X2)) = or(and(neg(X2),X),and(neg(X2),neg(neg(X2)))),
inference(congruence,[status(thm)],[c952]) ).
cnf(c954,plain,
and(or(and(neg(X3),X2),and(neg(X3),X3)),X) = and(or(and(neg(X3),X2),and(neg(X3),neg(neg(X3)))),X),
inference(congruence,[status(thm)],[c953]) ).
cnf(c955,plain,
or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(neg(X3),X3)),X)) = or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(neg(X3),neg(neg(X3)))),X)),
inference(congruence,[status(thm)],[c954]) ).
cnf(c956,plain,
and(neg(X3),or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(neg(X3),X3)),X))) = and(neg(X3),or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(neg(X3),neg(neg(X3)))),X))),
inference(congruence,[status(thm)],[c955]) ).
cnf(c957,plain,
and(neg(X3),or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(neg(X3),neg(neg(X3)))),X))) = and(neg(X3),X2),
inference(substitution,[status(thm)],[c518]) ).
cnf(c958,plain,
and(neg(X3),or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(neg(X3),neg(neg(X3)))),X))) = and(X2,neg(X3)),
inference(transitivity,[status(thm)],[c957,c930]) ).
cnf(c959,plain,
and(neg(X3),or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(neg(X3),X3)),X))) = and(X2,neg(X3)),
inference(transitivity,[status(thm)],[c956,c958]) ).
cnf(c960,plain,
and(neg(X3),or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(X3,neg(X3))),X))) = and(X2,neg(X3)),
inference(transitivity,[status(thm)],[c950,c959]) ).
cnf(c961,plain,
and(X2,neg(X3)) = and(neg(X3),or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(X3,neg(X3))),X))),
inference(symmetry,[status(thm)],[c960]) ).
cnf(c962,plain,
or(or(neg(X3),X4),and(X2,neg(X3))) = or(or(neg(X3),X4),and(neg(X3),or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(X3,neg(X3))),X)))),
inference(congruence,[status(thm)],[c961]) ).
cnf(c963,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c964,plain,
or(X2,X) = or(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c963]) ).
cnf(c965,plain,
or(or(X3,X2),and(X3,X)) = or(or(X3,neg(neg(X2))),and(X3,X)),
inference(congruence,[status(thm)],[c964]) ).
cnf(c966,plain,
and(X2,X) = and(X,X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c967,plain,
or(or(X3,neg(X2)),and(X3,X)) = or(or(X3,neg(X2)),and(X,X3)),
inference(congruence,[status(thm)],[c966]) ).
cnf(c968,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c969,plain,
and(neg(X2),X) = and(neg(X2),neg(neg(X))),
inference(congruence,[status(thm)],[c968]) ).
cnf(c970,plain,
and(or(X2,neg(X)),and(neg(X2),X)) = and(or(X2,neg(X)),and(neg(X2),neg(neg(X)))),
inference(congruence,[status(thm)],[c969]) ).
cnf(c971,plain,
or(X2,and(or(X2,neg(X)),and(neg(X2),X))) = or(X2,and(or(X2,neg(X)),and(neg(X2),neg(neg(X))))),
inference(congruence,[status(thm)],[c970]) ).
cnf(c972,plain,
and(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X)))) = and(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),neg(neg(X)))))),
inference(congruence,[status(thm)],[c971]) ).
cnf(c973,plain,
and(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),neg(neg(X)))))) = X2,
inference(substitution,[status(thm)],[c358]) ).
cnf(c974,plain,
and(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X)))) = X2,
inference(transitivity,[status(thm)],[c972,c973]) ).
cnf(c975,plain,
X2 = and(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X)))),
inference(symmetry,[status(thm)],[c974]) ).
cnf(c976,plain,
and(X,X3) = and(X,and(or(X3,neg(X2)),or(X3,and(or(X3,neg(X2)),and(neg(X3),X2))))),
inference(congruence,[status(thm)],[c975]) ).
cnf(c977,plain,
or(or(X3,neg(X2)),and(X,X3)) = or(or(X3,neg(X2)),and(X,and(or(X3,neg(X2)),or(X3,and(or(X3,neg(X2)),and(neg(X3),X2)))))),
inference(congruence,[status(thm)],[c976]) ).
cnf(c978,plain,
and(X2,X) = and(X,X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c979,plain,
and(X2,and(X3,X)) = and(X2,and(X,X3)),
inference(congruence,[status(thm)],[c978]) ).
cnf(c980,plain,
or(X3,and(X2,and(X3,X))) = or(X3,and(X2,and(X,X3))),
inference(congruence,[status(thm)],[c979]) ).
cnf(c981,plain,
X2 = and(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X)))),
inference(symmetry,[status(thm)],[c974]) ).
cnf(c982,plain,
and(X2,X3) = and(X2,and(or(X3,neg(X)),or(X3,and(or(X3,neg(X)),and(neg(X3),X))))),
inference(congruence,[status(thm)],[c981]) ).
cnf(c983,plain,
and(X3,and(X2,X4)) = and(X3,and(X2,and(or(X4,neg(X)),or(X4,and(or(X4,neg(X)),and(neg(X4),X)))))),
inference(congruence,[status(thm)],[c982]) ).
cnf(c984,plain,
or(X4,and(X3,and(X2,X4))) = or(X4,and(X3,and(X2,and(or(X4,neg(X)),or(X4,and(or(X4,neg(X)),and(neg(X4),X))))))),
inference(congruence,[status(thm)],[c983]) ).
cnf(c985,plain,
X2 = and(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X)))),
inference(symmetry,[status(thm)],[c974]) ).
cnf(c986,plain,
or(X4,and(X3,and(X2,and(or(X4,neg(X)),or(X4,and(or(X4,neg(X)),and(neg(X4),X))))))) = or(and(or(X4,neg(X)),or(X4,and(or(X4,neg(X)),and(neg(X4),X)))),and(X3,and(X2,and(or(X4,neg(X)),or(X4,and(or(X4,neg(X)),and(neg(X4),X))))))),
inference(congruence,[status(thm)],[c985]) ).
cnf(c987,plain,
and(X,and(X3,X2)) = and(and(X3,X2),X),
inference(substitution,[status(thm)],[c934]) ).
cnf(c988,plain,
and(X2,and(X,and(X4,X3))) = and(X2,and(and(X4,X3),X)),
inference(congruence,[status(thm)],[c987]) ).
cnf(c989,plain,
or(and(X4,X3),and(X2,and(X,and(X4,X3)))) = or(and(X4,X3),and(X2,and(and(X4,X3),X))),
inference(congruence,[status(thm)],[c988]) ).
cnf(c990,plain,
and(X2,and(and(X4,X3),X)) = and(and(and(X4,X3),X),X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c991,plain,
or(and(X4,X3),and(X2,and(and(X4,X3),X))) = or(and(X4,X3),and(and(and(X4,X3),X),X2)),
inference(congruence,[status(thm)],[c990]) ).
cnf(c992,plain,
and(X2,X) = and(X,X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c993,plain,
or(and(X4,X3),and(and(and(X4,X3),X),X2)) = or(and(X3,X4),and(and(and(X4,X3),X),X2)),
inference(congruence,[status(thm)],[c992]) ).
cnf(c994,plain,
and(X2,X) = and(X,X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c995,plain,
and(and(X3,X2),X) = and(and(X2,X3),X),
inference(congruence,[status(thm)],[c994]) ).
cnf(c996,plain,
and(and(and(X4,X3),X),X2) = and(and(and(X3,X4),X),X2),
inference(congruence,[status(thm)],[c995]) ).
cnf(c997,plain,
or(and(X3,X4),and(and(and(X4,X3),X),X2)) = or(and(X3,X4),and(and(and(X3,X4),X),X2)),
inference(congruence,[status(thm)],[c996]) ).
cnf(c998,plain,
or(and(X3,X4),and(and(and(X3,X4),X),X2)) = or(and(and(and(X3,X4),X),X2),and(X3,X4)),
inference(substitution,[status(thm)],[c913]) ).
cnf(c999,plain,
or(X2,X) = f(neg(X2),neg(X)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c1000,plain,
and(X2,or(X2,X)) = and(X2,f(neg(X2),neg(X))),
inference(congruence,[status(thm)],[c999]) ).
cnf(c1001,plain,
or(and(X2,or(X2,X)),X2) = or(and(X2,f(neg(X2),neg(X))),X2),
inference(congruence,[status(thm)],[c1000]) ).
cnf(c1002,plain,
and(X2,or(and(X2,or(X2,X)),X2)) = and(X2,or(and(X2,f(neg(X2),neg(X))),X2)),
inference(congruence,[status(thm)],[c1001]) ).
cnf(c1003,plain,
neg(and(neg(X2),neg(X))) = f(neg(X2),neg(X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1004,plain,
f(neg(X2),neg(X)) = neg(and(neg(X2),neg(X))),
inference(symmetry,[status(thm)],[c1003]) ).
cnf(c1005,plain,
and(X2,f(neg(X2),neg(X))) = and(X2,neg(and(neg(X2),neg(X)))),
inference(congruence,[status(thm)],[c1004]) ).
cnf(c1006,plain,
or(and(X2,f(neg(X2),neg(X))),X2) = or(and(X2,neg(and(neg(X2),neg(X)))),X2),
inference(congruence,[status(thm)],[c1005]) ).
cnf(c1007,plain,
and(X2,or(and(X2,f(neg(X2),neg(X))),X2)) = and(X2,or(and(X2,neg(and(neg(X2),neg(X)))),X2)),
inference(congruence,[status(thm)],[c1006]) ).
cnf(c1008,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1009,plain,
and(X2,neg(and(neg(X2),neg(X)))) = and(neg(neg(X2)),neg(and(neg(X2),neg(X)))),
inference(congruence,[status(thm)],[c1008]) ).
cnf(c1010,plain,
or(and(X2,neg(and(neg(X2),neg(X)))),X2) = or(and(neg(neg(X2)),neg(and(neg(X2),neg(X)))),X2),
inference(congruence,[status(thm)],[c1009]) ).
cnf(c1011,plain,
and(X2,or(and(X2,neg(and(neg(X2),neg(X)))),X2)) = and(X2,or(and(neg(neg(X2)),neg(and(neg(X2),neg(X)))),X2)),
inference(congruence,[status(thm)],[c1010]) ).
cnf(c1012,plain,
neg(or(neg(X2),and(neg(X2),neg(X)))) = and(neg(neg(X2)),neg(and(neg(X2),neg(X)))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1013,plain,
and(neg(neg(X2)),neg(and(neg(X2),neg(X)))) = neg(or(neg(X2),and(neg(X2),neg(X)))),
inference(symmetry,[status(thm)],[c1012]) ).
cnf(c1014,plain,
or(and(neg(neg(X2)),neg(and(neg(X2),neg(X)))),X2) = or(neg(or(neg(X2),and(neg(X2),neg(X)))),X2),
inference(congruence,[status(thm)],[c1013]) ).
cnf(c1015,plain,
and(X2,or(and(neg(neg(X2)),neg(and(neg(X2),neg(X)))),X2)) = and(X2,or(neg(or(neg(X2),and(neg(X2),neg(X)))),X2)),
inference(congruence,[status(thm)],[c1014]) ).
cnf(c1016,plain,
f(or(neg(X2),and(neg(X2),neg(X))),neg(X2)) = or(neg(or(neg(X2),and(neg(X2),neg(X)))),X2),
inference(substitution,[status(thm)],[c85]) ).
cnf(c1017,plain,
or(neg(or(neg(X2),and(neg(X2),neg(X)))),X2) = f(or(neg(X2),and(neg(X2),neg(X))),neg(X2)),
inference(symmetry,[status(thm)],[c1016]) ).
cnf(c1018,plain,
and(X2,or(neg(or(neg(X2),and(neg(X2),neg(X)))),X2)) = and(X2,f(or(neg(X2),and(neg(X2),neg(X))),neg(X2))),
inference(congruence,[status(thm)],[c1017]) ).
cnf(c1019,plain,
neg(and(or(neg(X2),and(neg(X2),neg(X))),neg(X2))) = f(or(neg(X2),and(neg(X2),neg(X))),neg(X2)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1020,plain,
f(or(neg(X2),and(neg(X2),neg(X))),neg(X2)) = neg(and(or(neg(X2),and(neg(X2),neg(X))),neg(X2))),
inference(symmetry,[status(thm)],[c1019]) ).
cnf(c1021,plain,
and(X2,f(or(neg(X2),and(neg(X2),neg(X))),neg(X2))) = and(X2,neg(and(or(neg(X2),and(neg(X2),neg(X))),neg(X2)))),
inference(congruence,[status(thm)],[c1020]) ).
cnf(c1022,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1023,plain,
and(X2,neg(and(or(neg(X2),and(neg(X2),neg(X))),neg(X2)))) = and(neg(neg(X2)),neg(and(or(neg(X2),and(neg(X2),neg(X))),neg(X2)))),
inference(congruence,[status(thm)],[c1022]) ).
cnf(c1024,plain,
neg(or(neg(X2),and(or(neg(X2),and(neg(X2),neg(X))),neg(X2)))) = and(neg(neg(X2)),neg(and(or(neg(X2),and(neg(X2),neg(X))),neg(X2)))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1025,plain,
and(neg(neg(X2)),neg(and(or(neg(X2),and(neg(X2),neg(X))),neg(X2)))) = neg(or(neg(X2),and(or(neg(X2),and(neg(X2),neg(X))),neg(X2)))),
inference(symmetry,[status(thm)],[c1024]) ).
cnf(c1026,plain,
neg(neg(neg(X))) = neg(X),
inference(substitution,[status(thm)],[c79]) ).
cnf(c1027,plain,
neg(X) = neg(neg(neg(X))),
inference(symmetry,[status(thm)],[c1026]) ).
cnf(c1028,plain,
and(neg(X2),neg(X)) = and(neg(neg(neg(X2))),neg(X)),
inference(congruence,[status(thm)],[c1027]) ).
cnf(c1029,plain,
or(neg(X2),and(neg(X2),neg(X))) = or(neg(X2),and(neg(neg(neg(X2))),neg(X))),
inference(congruence,[status(thm)],[c1028]) ).
cnf(c1030,plain,
and(or(neg(X2),and(neg(X2),neg(X))),neg(X2)) = and(or(neg(X2),and(neg(neg(neg(X2))),neg(X))),neg(X2)),
inference(congruence,[status(thm)],[c1029]) ).
cnf(c1031,plain,
or(neg(X2),and(or(neg(X2),and(neg(X2),neg(X))),neg(X2))) = or(neg(X2),and(or(neg(X2),and(neg(neg(neg(X2))),neg(X))),neg(X2))),
inference(congruence,[status(thm)],[c1030]) ).
cnf(c1032,plain,
neg(or(neg(neg(X2)),X)) = and(neg(neg(neg(X2))),neg(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1033,plain,
and(neg(neg(neg(X2))),neg(X)) = neg(or(neg(neg(X2)),X)),
inference(symmetry,[status(thm)],[c1032]) ).
cnf(c1034,plain,
or(neg(X2),and(neg(neg(neg(X2))),neg(X))) = or(neg(X2),neg(or(neg(neg(X2)),X))),
inference(congruence,[status(thm)],[c1033]) ).
cnf(c1035,plain,
and(or(neg(X2),and(neg(neg(neg(X2))),neg(X))),neg(X2)) = and(or(neg(X2),neg(or(neg(neg(X2)),X))),neg(X2)),
inference(congruence,[status(thm)],[c1034]) ).
cnf(c1036,plain,
or(neg(X2),and(or(neg(X2),and(neg(neg(neg(X2))),neg(X))),neg(X2))) = or(neg(X2),and(or(neg(X2),neg(or(neg(neg(X2)),X))),neg(X2))),
inference(congruence,[status(thm)],[c1035]) ).
cnf(c1037,plain,
f(X2,or(neg(neg(X2)),X)) = or(neg(X2),neg(or(neg(neg(X2)),X))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1038,plain,
or(neg(X2),neg(or(neg(neg(X2)),X))) = f(X2,or(neg(neg(X2)),X)),
inference(symmetry,[status(thm)],[c1037]) ).
cnf(c1039,plain,
and(or(neg(X2),neg(or(neg(neg(X2)),X))),neg(X2)) = and(f(X2,or(neg(neg(X2)),X)),neg(X2)),
inference(congruence,[status(thm)],[c1038]) ).
cnf(c1040,plain,
or(neg(X2),and(or(neg(X2),neg(or(neg(neg(X2)),X))),neg(X2))) = or(neg(X2),and(f(X2,or(neg(neg(X2)),X)),neg(X2))),
inference(congruence,[status(thm)],[c1039]) ).
cnf(c1041,plain,
neg(f(f(X2,or(neg(neg(X2)),X)),neg(X2))) = and(f(X2,or(neg(neg(X2)),X)),neg(X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1042,plain,
and(f(X2,or(neg(neg(X2)),X)),neg(X2)) = neg(f(f(X2,or(neg(neg(X2)),X)),neg(X2))),
inference(symmetry,[status(thm)],[c1041]) ).
cnf(c1043,plain,
or(neg(X2),and(f(X2,or(neg(neg(X2)),X)),neg(X2))) = or(neg(X2),neg(f(f(X2,or(neg(neg(X2)),X)),neg(X2)))),
inference(congruence,[status(thm)],[c1042]) ).
cnf(c1044,plain,
f(X2,f(f(X2,or(neg(neg(X2)),X)),neg(X2))) = or(neg(X2),neg(f(f(X2,or(neg(neg(X2)),X)),neg(X2)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1045,plain,
or(neg(X2),neg(f(f(X2,or(neg(neg(X2)),X)),neg(X2)))) = f(X2,f(f(X2,or(neg(neg(X2)),X)),neg(X2))),
inference(symmetry,[status(thm)],[c1044]) ).
cnf(c1046,plain,
f(neg(X2),neg(X)) = or(neg(neg(X2)),X),
inference(substitution,[status(thm)],[c85]) ).
cnf(c1047,plain,
or(neg(neg(X2)),X) = f(neg(X2),neg(X)),
inference(symmetry,[status(thm)],[c1046]) ).
cnf(c1048,plain,
f(X2,or(neg(neg(X2)),X)) = f(X2,f(neg(X2),neg(X))),
inference(congruence,[status(thm)],[c1047]) ).
cnf(c1049,plain,
f(f(X2,or(neg(neg(X2)),X)),neg(X2)) = f(f(X2,f(neg(X2),neg(X))),neg(X2)),
inference(congruence,[status(thm)],[c1048]) ).
cnf(c1050,plain,
f(X2,f(f(X2,or(neg(neg(X2)),X)),neg(X2))) = f(X2,f(f(X2,f(neg(X2),neg(X))),neg(X2))),
inference(congruence,[status(thm)],[c1049]) ).
cnf(c1051,plain,
f(f(neg(neg(X)),X),f(f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),X)) = f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c1052,plain,
f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))) = f(f(neg(neg(X)),X),f(f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),X)),
inference(symmetry,[status(thm)],[c1051]) ).
cnf(c1053,plain,
f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))) = X,
inference(substitution,[status(thm)],[c213]) ).
cnf(c1054,plain,
f(f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),X) = f(X,X),
inference(congruence,[status(thm)],[c1053]) ).
cnf(c1055,plain,
f(f(neg(neg(X)),X),f(f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),X)) = f(f(neg(neg(X)),X),f(X,X)),
inference(congruence,[status(thm)],[c1054]) ).
cnf(c1056,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1057,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c1056]) ).
cnf(c1058,plain,
f(f(neg(neg(X)),X),f(X,X)) = f(f(neg(neg(X)),X),neg(X)),
inference(congruence,[status(thm)],[c1057]) ).
cnf(c1059,plain,
f(f(neg(neg(X)),X),f(f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),X)) = f(f(neg(neg(X)),X),neg(X)),
inference(transitivity,[status(thm)],[c1055,c1058]) ).
cnf(c1060,plain,
f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))) = f(f(neg(neg(X)),X),neg(X)),
inference(transitivity,[status(thm)],[c1052,c1059]) ).
cnf(c1061,plain,
f(f(neg(neg(X)),X),neg(X)) = f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),
inference(symmetry,[status(thm)],[c1060]) ).
cnf(c1062,plain,
f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))) = X,
inference(substitution,[status(thm)],[c213]) ).
cnf(c1063,plain,
f(f(neg(neg(X)),X),neg(X)) = X,
inference(transitivity,[status(thm)],[c1061,c1062]) ).
cnf(c1064,plain,
X = f(f(neg(neg(X)),X),neg(X)),
inference(symmetry,[status(thm)],[c1063]) ).
cnf(c1065,plain,
f(X2,f(neg(X2),X)) = f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),
inference(congruence,[status(thm)],[c1064]) ).
cnf(c1066,plain,
f(f(X2,f(neg(X2),X)),neg(X2)) = f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2)),
inference(congruence,[status(thm)],[c1065]) ).
cnf(c1067,plain,
f(X2,f(f(X2,f(neg(X2),X)),neg(X2))) = f(X2,f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2))),
inference(congruence,[status(thm)],[c1066]) ).
cnf(c1068,plain,
X = f(f(neg(neg(X)),X),neg(X)),
inference(symmetry,[status(thm)],[c1063]) ).
cnf(c1069,plain,
f(X2,f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2))) = f(f(f(neg(neg(X2)),X2),neg(X2)),f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2))),
inference(congruence,[status(thm)],[c1068]) ).
cnf(c1070,plain,
f(f(f(neg(neg(X2)),X2),neg(X2)),f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2))) = f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c1071,plain,
f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)) = f(X2,f(neg(X2),X)),
inference(congruence,[status(thm)],[c1063]) ).
cnf(c1072,plain,
f(f(f(neg(neg(X2)),X2),neg(X2)),f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2))) = f(X2,f(neg(X2),X)),
inference(transitivity,[status(thm)],[c1070,c1071]) ).
cnf(c1073,plain,
f(X2,f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2))) = f(X2,f(neg(X2),X)),
inference(transitivity,[status(thm)],[c1069,c1072]) ).
cnf(c1074,plain,
f(X2,f(f(X2,f(neg(X2),X)),neg(X2))) = f(X2,f(neg(X2),X)),
inference(transitivity,[status(thm)],[c1067,c1073]) ).
cnf(c1075,plain,
f(X2,f(f(X2,f(neg(X2),neg(X))),neg(X2))) = f(X2,f(neg(X2),neg(X))),
inference(substitution,[status(thm)],[c1074]) ).
cnf(c1076,plain,
f(X2,f(neg(X2),neg(X))) = or(neg(X2),neg(f(neg(X2),neg(X)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1077,plain,
neg(f(neg(X2),neg(X))) = and(neg(X2),neg(X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1078,plain,
or(neg(X2),neg(f(neg(X2),neg(X)))) = or(neg(X2),and(neg(X2),neg(X))),
inference(congruence,[status(thm)],[c1077]) ).
cnf(c1079,plain,
f(X2,f(neg(X2),neg(X))) = or(neg(X2),and(neg(X2),neg(X))),
inference(transitivity,[status(thm)],[c1076,c1078]) ).
cnf(c1080,plain,
f(X2,f(f(X2,f(neg(X2),neg(X))),neg(X2))) = or(neg(X2),and(neg(X2),neg(X))),
inference(transitivity,[status(thm)],[c1075,c1079]) ).
cnf(c1081,plain,
f(X2,f(f(X2,or(neg(neg(X2)),X)),neg(X2))) = or(neg(X2),and(neg(X2),neg(X))),
inference(transitivity,[status(thm)],[c1050,c1080]) ).
cnf(c1082,plain,
or(neg(X2),neg(f(f(X2,or(neg(neg(X2)),X)),neg(X2)))) = or(neg(X2),and(neg(X2),neg(X))),
inference(transitivity,[status(thm)],[c1045,c1081]) ).
cnf(c1083,plain,
or(neg(X2),and(f(X2,or(neg(neg(X2)),X)),neg(X2))) = or(neg(X2),and(neg(X2),neg(X))),
inference(transitivity,[status(thm)],[c1043,c1082]) ).
cnf(c1084,plain,
or(neg(X2),and(or(neg(X2),neg(or(neg(neg(X2)),X))),neg(X2))) = or(neg(X2),and(neg(X2),neg(X))),
inference(transitivity,[status(thm)],[c1040,c1083]) ).
cnf(c1085,plain,
or(neg(X2),and(or(neg(X2),and(neg(neg(neg(X2))),neg(X))),neg(X2))) = or(neg(X2),and(neg(X2),neg(X))),
inference(transitivity,[status(thm)],[c1036,c1084]) ).
cnf(c1086,plain,
or(neg(X2),and(or(neg(X2),and(neg(X2),neg(X))),neg(X2))) = or(neg(X2),and(neg(X2),neg(X))),
inference(transitivity,[status(thm)],[c1031,c1085]) ).
cnf(c1087,plain,
neg(or(neg(X2),and(or(neg(X2),and(neg(X2),neg(X))),neg(X2)))) = neg(or(neg(X2),and(neg(X2),neg(X)))),
inference(congruence,[status(thm)],[c1086]) ).
cnf(c1088,plain,
neg(or(neg(X2),and(neg(X2),neg(X)))) = and(neg(neg(X2)),neg(and(neg(X2),neg(X)))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1089,plain,
and(neg(neg(X2)),neg(and(neg(X2),neg(X)))) = and(X2,neg(and(neg(X2),neg(X)))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c1090,plain,
neg(and(neg(X2),neg(X))) = f(neg(X2),neg(X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1091,plain,
and(X2,neg(and(neg(X2),neg(X)))) = and(X2,f(neg(X2),neg(X))),
inference(congruence,[status(thm)],[c1090]) ).
cnf(c1092,plain,
and(X2,f(neg(X2),neg(X))) = and(X2,or(X2,X)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c1093,plain,
and(X2,neg(and(neg(X2),neg(X)))) = and(X2,or(X2,X)),
inference(transitivity,[status(thm)],[c1091,c1092]) ).
cnf(c1094,plain,
and(neg(neg(X2)),neg(and(neg(X2),neg(X)))) = and(X2,or(X2,X)),
inference(transitivity,[status(thm)],[c1089,c1093]) ).
cnf(c1095,plain,
neg(or(neg(X2),and(neg(X2),neg(X)))) = and(X2,or(X2,X)),
inference(transitivity,[status(thm)],[c1088,c1094]) ).
cnf(c1096,plain,
neg(or(neg(X2),and(or(neg(X2),and(neg(X2),neg(X))),neg(X2)))) = and(X2,or(X2,X)),
inference(transitivity,[status(thm)],[c1087,c1095]) ).
cnf(c1097,plain,
and(neg(neg(X2)),neg(and(or(neg(X2),and(neg(X2),neg(X))),neg(X2)))) = and(X2,or(X2,X)),
inference(transitivity,[status(thm)],[c1025,c1096]) ).
cnf(c1098,plain,
and(X2,neg(and(or(neg(X2),and(neg(X2),neg(X))),neg(X2)))) = and(X2,or(X2,X)),
inference(transitivity,[status(thm)],[c1023,c1097]) ).
cnf(c1099,plain,
and(X2,f(or(neg(X2),and(neg(X2),neg(X))),neg(X2))) = and(X2,or(X2,X)),
inference(transitivity,[status(thm)],[c1021,c1098]) ).
cnf(c1100,plain,
and(X2,or(neg(or(neg(X2),and(neg(X2),neg(X)))),X2)) = and(X2,or(X2,X)),
inference(transitivity,[status(thm)],[c1018,c1099]) ).
cnf(c1101,plain,
and(X2,or(and(neg(neg(X2)),neg(and(neg(X2),neg(X)))),X2)) = and(X2,or(X2,X)),
inference(transitivity,[status(thm)],[c1015,c1100]) ).
cnf(c1102,plain,
and(X2,or(and(X2,neg(and(neg(X2),neg(X)))),X2)) = and(X2,or(X2,X)),
inference(transitivity,[status(thm)],[c1011,c1101]) ).
cnf(c1103,plain,
and(X2,or(and(X2,f(neg(X2),neg(X))),X2)) = and(X2,or(X2,X)),
inference(transitivity,[status(thm)],[c1007,c1102]) ).
cnf(c1104,plain,
and(X2,or(and(X2,or(X2,X)),X2)) = and(X2,or(X2,X)),
inference(transitivity,[status(thm)],[c1002,c1103]) ).
cnf(c1105,plain,
and(X2,or(X2,X)) = and(X2,or(and(X2,or(X2,X)),X2)),
inference(symmetry,[status(thm)],[c1104]) ).
cnf(c1106,plain,
or(and(X2,or(X2,X)),X2) = X2,
inference(substitution,[status(thm)],[c649]) ).
cnf(c1107,plain,
and(X2,or(and(X2,or(X2,X)),X2)) = and(X2,X2),
inference(congruence,[status(thm)],[c1106]) ).
cnf(c1108,plain,
and(X,X) = X,
inference(transitivity,[status(thm)],[c122,c79]) ).
cnf(c1109,plain,
and(X2,or(and(X2,or(X2,X)),X2)) = X2,
inference(transitivity,[status(thm)],[c1107,c1108]) ).
cnf(c1110,plain,
and(X2,or(X2,X)) = X2,
inference(transitivity,[status(thm)],[c1105,c1109]) ).
cnf(c1111,plain,
and(and(X2,X3),or(and(X2,X3),neg(X))) = and(X2,X3),
inference(substitution,[status(thm)],[c1110]) ).
cnf(c1112,plain,
and(X2,X3) = and(and(X2,X3),or(and(X2,X3),neg(X))),
inference(symmetry,[status(thm)],[c1111]) ).
cnf(c1113,plain,
or(and(and(and(X3,X4),X),X2),and(X3,X4)) = or(and(and(and(X3,X4),X),X2),and(and(X3,X4),or(and(X3,X4),neg(X)))),
inference(congruence,[status(thm)],[c1112]) ).
cnf(c1114,plain,
or(X2,and(X,neg(X))) = or(and(X,neg(X)),X2),
inference(substitution,[status(thm)],[c913]) ).
cnf(c1115,plain,
f(neg(X),neg(X)) = or(X,X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c1116,plain,
or(X,X) = f(neg(X),neg(X)),
inference(symmetry,[status(thm)],[c1115]) ).
cnf(c1117,plain,
neg(neg(X)) = f(neg(X),neg(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1118,plain,
f(neg(X),neg(X)) = neg(neg(X)),
inference(symmetry,[status(thm)],[c1117]) ).
cnf(c1119,plain,
f(neg(X),neg(X)) = X,
inference(transitivity,[status(thm)],[c1118,c79]) ).
cnf(c1120,plain,
or(X,X) = X,
inference(transitivity,[status(thm)],[c1116,c1119]) ).
cnf(c1121,plain,
or(and(X2,or(neg(X2),and(X2,or(X,neg(X))))),and(X2,or(neg(X2),and(X2,or(X,neg(X)))))) = and(X2,or(neg(X2),and(X2,or(X,neg(X))))),
inference(substitution,[status(thm)],[c1120]) ).
cnf(c1122,plain,
and(X2,or(neg(X2),and(X2,or(X,neg(X))))) = or(and(X2,or(neg(X2),and(X2,or(X,neg(X))))),and(X2,or(neg(X2),and(X2,or(X,neg(X)))))),
inference(symmetry,[status(thm)],[c1121]) ).
cnf(c1123,plain,
or(neg(X2),and(X2,or(X,neg(X)))) = or(and(X2,or(X,neg(X))),neg(X2)),
inference(substitution,[status(thm)],[c913]) ).
cnf(c1124,plain,
and(X2,or(neg(X2),and(X2,or(X,neg(X))))) = and(X2,or(and(X2,or(X,neg(X))),neg(X2))),
inference(congruence,[status(thm)],[c1123]) ).
cnf(c1125,plain,
or(and(X3,X2),and(X3,or(neg(X3),and(X3,or(X,neg(X)))))) = or(and(X3,X2),and(X3,or(and(X3,or(X,neg(X))),neg(X3)))),
inference(congruence,[status(thm)],[c1124]) ).
cnf(c1126,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1127,plain,
and(X2,X) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c1126]) ).
cnf(c1128,plain,
or(and(X2,X),X) = or(and(X2,neg(neg(X))),X),
inference(congruence,[status(thm)],[c1127]) ).
cnf(c1129,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1130,plain,
and(X2,neg(neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(congruence,[status(thm)],[c1129]) ).
cnf(c1131,plain,
or(and(X2,neg(neg(X))),X) = or(and(neg(neg(X2)),neg(neg(X))),X),
inference(congruence,[status(thm)],[c1130]) ).
cnf(c1132,plain,
neg(or(neg(X2),neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1133,plain,
and(neg(neg(X2)),neg(neg(X))) = neg(or(neg(X2),neg(X))),
inference(symmetry,[status(thm)],[c1132]) ).
cnf(c1134,plain,
or(and(neg(neg(X2)),neg(neg(X))),X) = or(neg(or(neg(X2),neg(X))),X),
inference(congruence,[status(thm)],[c1133]) ).
cnf(c1135,plain,
f(or(neg(X2),neg(X)),neg(X)) = or(neg(or(neg(X2),neg(X))),X),
inference(substitution,[status(thm)],[c85]) ).
cnf(c1136,plain,
or(neg(or(neg(X2),neg(X))),X) = f(or(neg(X2),neg(X)),neg(X)),
inference(symmetry,[status(thm)],[c1135]) ).
cnf(c1137,plain,
neg(and(or(neg(X2),neg(X)),neg(X))) = f(or(neg(X2),neg(X)),neg(X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1138,plain,
f(or(neg(X2),neg(X)),neg(X)) = neg(and(or(neg(X2),neg(X)),neg(X))),
inference(symmetry,[status(thm)],[c1137]) ).
cnf(c1139,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1140,plain,
neg(and(X2,X)) = neg(neg(f(X2,X))),
inference(congruence,[status(thm)],[c1139]) ).
cnf(c1141,plain,
f(neg(and(X2,X)),f(X2,X)) = f(neg(neg(f(X2,X))),f(X2,X)),
inference(congruence,[status(thm)],[c1140]) ).
cnf(c1142,plain,
f(and(X2,X),f(neg(and(X2,X)),f(X2,X))) = f(and(X2,X),f(neg(neg(f(X2,X))),f(X2,X))),
inference(congruence,[status(thm)],[c1141]) ).
cnf(c1143,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1144,plain,
f(and(X2,X),f(neg(neg(f(X2,X))),f(X2,X))) = f(neg(f(X2,X)),f(neg(neg(f(X2,X))),f(X2,X))),
inference(congruence,[status(thm)],[c1143]) ).
cnf(c1145,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1146,plain,
f(neg(X),f(neg(neg(X)),X)) = f(f(X,X),f(neg(neg(X)),X)),
inference(congruence,[status(thm)],[c1145]) ).
cnf(c1147,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1148,plain,
neg(neg(X)) = neg(f(X,X)),
inference(congruence,[status(thm)],[c1147]) ).
cnf(c1149,plain,
f(neg(neg(X)),X) = f(neg(f(X,X)),X),
inference(congruence,[status(thm)],[c1148]) ).
cnf(c1150,plain,
f(f(X,X),f(neg(neg(X)),X)) = f(f(X,X),f(neg(f(X,X)),X)),
inference(congruence,[status(thm)],[c1149]) ).
cnf(c1151,plain,
neg(f(X,X)) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1152,plain,
f(neg(f(X,X)),X) = f(f(f(X,X),f(X,X)),X),
inference(congruence,[status(thm)],[c1151]) ).
cnf(c1153,plain,
f(f(X,X),f(neg(f(X,X)),X)) = f(f(X,X),f(f(f(X,X),f(X,X)),X)),
inference(congruence,[status(thm)],[c1152]) ).
cnf(c1154,plain,
f(f(X,X),f(f(f(X,X),f(X,X)),X)) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c1155,plain,
neg(f(X,X)) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1156,plain,
f(f(X,X),f(X,X)) = neg(f(X,X)),
inference(symmetry,[status(thm)],[c1155]) ).
cnf(c1157,plain,
neg(f(X,X)) = and(X,X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1158,plain,
neg(f(X,X)) = neg(neg(X)),
inference(transitivity,[status(thm)],[c1157,c122]) ).
cnf(c1159,plain,
f(f(X,X),f(X,X)) = neg(neg(X)),
inference(transitivity,[status(thm)],[c1156,c1158]) ).
cnf(c1160,plain,
f(f(X,X),f(f(f(X,X),f(X,X)),X)) = neg(neg(X)),
inference(transitivity,[status(thm)],[c1154,c1159]) ).
cnf(c1161,plain,
f(f(X,X),f(neg(f(X,X)),X)) = neg(neg(X)),
inference(transitivity,[status(thm)],[c1153,c1160]) ).
cnf(c1162,plain,
f(f(X,X),f(neg(neg(X)),X)) = neg(neg(X)),
inference(transitivity,[status(thm)],[c1150,c1161]) ).
cnf(c1163,plain,
f(neg(X),f(neg(neg(X)),X)) = neg(neg(X)),
inference(transitivity,[status(thm)],[c1146,c1162]) ).
cnf(c1164,plain,
f(neg(f(X2,X)),f(neg(neg(f(X2,X))),f(X2,X))) = neg(neg(f(X2,X))),
inference(substitution,[status(thm)],[c1163]) ).
cnf(c1165,plain,
neg(neg(f(X2,X))) = neg(and(X2,X)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1166,plain,
f(neg(f(X2,X)),f(neg(neg(f(X2,X))),f(X2,X))) = neg(and(X2,X)),
inference(transitivity,[status(thm)],[c1164,c1165]) ).
cnf(c1167,plain,
f(and(X2,X),f(neg(neg(f(X2,X))),f(X2,X))) = neg(and(X2,X)),
inference(transitivity,[status(thm)],[c1144,c1166]) ).
cnf(c1168,plain,
f(and(X2,X),f(neg(and(X2,X)),f(X2,X))) = neg(and(X2,X)),
inference(transitivity,[status(thm)],[c1142,c1167]) ).
cnf(c1169,plain,
f(and(or(neg(X2),neg(X)),neg(X)),f(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X)))) = neg(and(or(neg(X2),neg(X)),neg(X))),
inference(substitution,[status(thm)],[c1168]) ).
cnf(c1170,plain,
neg(and(or(neg(X2),neg(X)),neg(X))) = f(and(or(neg(X2),neg(X)),neg(X)),f(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X)))),
inference(symmetry,[status(thm)],[c1169]) ).
cnf(c1171,plain,
f(and(or(neg(X2),neg(X)),neg(X)),f(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X)))) = f(neg(X),f(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X)))),
inference(congruence,[status(thm)],[c787]) ).
cnf(c1172,plain,
f(neg(X),f(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X)))) = or(X,neg(f(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X))))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c1173,plain,
neg(f(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X)))) = and(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1174,plain,
or(X,neg(f(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X))))) = or(X,and(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X)))),
inference(congruence,[status(thm)],[c1173]) ).
cnf(c1175,plain,
neg(and(or(neg(X2),neg(X)),neg(X))) = f(or(neg(X2),neg(X)),neg(X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1176,plain,
and(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X))) = and(f(or(neg(X2),neg(X)),neg(X)),f(or(neg(X2),neg(X)),neg(X))),
inference(congruence,[status(thm)],[c1175]) ).
cnf(c1177,plain,
or(X,and(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X)))) = or(X,and(f(or(neg(X2),neg(X)),neg(X)),f(or(neg(X2),neg(X)),neg(X)))),
inference(congruence,[status(thm)],[c1176]) ).
cnf(c1178,plain,
and(f(or(neg(X2),neg(X)),neg(X)),f(or(neg(X2),neg(X)),neg(X))) = neg(neg(f(or(neg(X2),neg(X)),neg(X)))),
inference(substitution,[status(thm)],[c122]) ).
cnf(c1179,plain,
or(X,and(f(or(neg(X2),neg(X)),neg(X)),f(or(neg(X2),neg(X)),neg(X)))) = or(X,neg(neg(f(or(neg(X2),neg(X)),neg(X))))),
inference(congruence,[status(thm)],[c1178]) ).
cnf(c1180,plain,
neg(neg(f(or(neg(X2),neg(X)),neg(X)))) = f(or(neg(X2),neg(X)),neg(X)),
inference(substitution,[status(thm)],[c79]) ).
cnf(c1181,plain,
or(X,neg(neg(f(or(neg(X2),neg(X)),neg(X))))) = or(X,f(or(neg(X2),neg(X)),neg(X))),
inference(congruence,[status(thm)],[c1180]) ).
cnf(c1182,plain,
f(or(neg(X2),neg(X)),neg(X)) = or(neg(or(neg(X2),neg(X))),X),
inference(substitution,[status(thm)],[c85]) ).
cnf(c1183,plain,
or(X,f(or(neg(X2),neg(X)),neg(X))) = or(X,or(neg(or(neg(X2),neg(X))),X)),
inference(congruence,[status(thm)],[c1182]) ).
cnf(c1184,plain,
neg(or(neg(X2),neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1185,plain,
or(neg(or(neg(X2),neg(X))),X) = or(and(neg(neg(X2)),neg(neg(X))),X),
inference(congruence,[status(thm)],[c1184]) ).
cnf(c1186,plain,
or(X,or(neg(or(neg(X2),neg(X))),X)) = or(X,or(and(neg(neg(X2)),neg(neg(X))),X)),
inference(congruence,[status(thm)],[c1185]) ).
cnf(c1187,plain,
and(neg(neg(X2)),neg(neg(X))) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c1188,plain,
or(and(neg(neg(X2)),neg(neg(X))),X) = or(and(X2,neg(neg(X))),X),
inference(congruence,[status(thm)],[c1187]) ).
cnf(c1189,plain,
or(X,or(and(neg(neg(X2)),neg(neg(X))),X)) = or(X,or(and(X2,neg(neg(X))),X)),
inference(congruence,[status(thm)],[c1188]) ).
cnf(c1190,plain,
and(X2,neg(neg(X))) = and(X2,X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c1191,plain,
or(and(X2,neg(neg(X))),X) = or(and(X2,X),X),
inference(congruence,[status(thm)],[c1190]) ).
cnf(c1192,plain,
or(X,or(and(X2,neg(neg(X))),X)) = or(X,or(and(X2,X),X)),
inference(congruence,[status(thm)],[c1191]) ).
cnf(c1193,plain,
or(X,or(and(X2,X),X)) = X,
inference(substitution,[status(thm)],[c768]) ).
cnf(c1194,plain,
or(X,or(and(X2,neg(neg(X))),X)) = X,
inference(transitivity,[status(thm)],[c1192,c1193]) ).
cnf(c1195,plain,
or(X,or(and(neg(neg(X2)),neg(neg(X))),X)) = X,
inference(transitivity,[status(thm)],[c1189,c1194]) ).
cnf(c1196,plain,
or(X,or(neg(or(neg(X2),neg(X))),X)) = X,
inference(transitivity,[status(thm)],[c1186,c1195]) ).
cnf(c1197,plain,
or(X,f(or(neg(X2),neg(X)),neg(X))) = X,
inference(transitivity,[status(thm)],[c1183,c1196]) ).
cnf(c1198,plain,
or(X,neg(neg(f(or(neg(X2),neg(X)),neg(X))))) = X,
inference(transitivity,[status(thm)],[c1181,c1197]) ).
cnf(c1199,plain,
or(X,and(f(or(neg(X2),neg(X)),neg(X)),f(or(neg(X2),neg(X)),neg(X)))) = X,
inference(transitivity,[status(thm)],[c1179,c1198]) ).
cnf(c1200,plain,
or(X,and(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X)))) = X,
inference(transitivity,[status(thm)],[c1177,c1199]) ).
cnf(c1201,plain,
or(X,neg(f(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X))))) = X,
inference(transitivity,[status(thm)],[c1174,c1200]) ).
cnf(c1202,plain,
f(neg(X),f(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X)))) = X,
inference(transitivity,[status(thm)],[c1172,c1201]) ).
cnf(c1203,plain,
f(and(or(neg(X2),neg(X)),neg(X)),f(neg(and(or(neg(X2),neg(X)),neg(X))),f(or(neg(X2),neg(X)),neg(X)))) = X,
inference(transitivity,[status(thm)],[c1171,c1202]) ).
cnf(c1204,plain,
neg(and(or(neg(X2),neg(X)),neg(X))) = X,
inference(transitivity,[status(thm)],[c1170,c1203]) ).
cnf(c1205,plain,
f(or(neg(X2),neg(X)),neg(X)) = X,
inference(transitivity,[status(thm)],[c1138,c1204]) ).
cnf(c1206,plain,
or(neg(or(neg(X2),neg(X))),X) = X,
inference(transitivity,[status(thm)],[c1136,c1205]) ).
cnf(c1207,plain,
or(and(neg(neg(X2)),neg(neg(X))),X) = X,
inference(transitivity,[status(thm)],[c1134,c1206]) ).
cnf(c1208,plain,
or(and(X2,neg(neg(X))),X) = X,
inference(transitivity,[status(thm)],[c1131,c1207]) ).
cnf(c1209,plain,
or(and(X2,X),X) = X,
inference(transitivity,[status(thm)],[c1128,c1208]) ).
cnf(c1210,plain,
or(and(X,X2),X2) = X2,
inference(substitution,[status(thm)],[c1209]) ).
cnf(c1211,plain,
X2 = or(and(X,X2),X2),
inference(symmetry,[status(thm)],[c1210]) ).
cnf(c1212,plain,
and(X3,X2) = and(or(and(X,X3),X3),X2),
inference(congruence,[status(thm)],[c1211]) ).
cnf(c1213,plain,
or(and(X3,X2),and(X3,or(and(X3,or(X,neg(X))),neg(X3)))) = or(and(or(and(X,X3),X3),X2),and(X3,or(and(X3,or(X,neg(X))),neg(X3)))),
inference(congruence,[status(thm)],[c1212]) ).
cnf(c1214,plain,
neg(f(X,X)) = and(X,X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1215,plain,
and(X,X) = neg(f(X,X)),
inference(symmetry,[status(thm)],[c1214]) ).
cnf(c1216,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1217,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c1216]) ).
cnf(c1218,plain,
neg(f(X,X)) = neg(neg(X)),
inference(congruence,[status(thm)],[c1217]) ).
cnf(c1219,plain,
neg(f(X,X)) = X,
inference(transitivity,[status(thm)],[c1218,c79]) ).
cnf(c1220,plain,
and(X,X) = X,
inference(transitivity,[status(thm)],[c1215,c1219]) ).
cnf(c1221,plain,
X = and(X,X),
inference(symmetry,[status(thm)],[c1220]) ).
cnf(c1222,plain,
or(and(X,X2),X2) = or(and(X,X2),and(X2,X2)),
inference(congruence,[status(thm)],[c1221]) ).
cnf(c1223,plain,
and(or(and(X,X3),X3),X2) = and(or(and(X,X3),and(X3,X3)),X2),
inference(congruence,[status(thm)],[c1222]) ).
cnf(c1224,plain,
or(and(or(and(X,X3),X3),X2),and(X3,or(and(X3,or(X,neg(X))),neg(X3)))) = or(and(or(and(X,X3),and(X3,X3)),X2),and(X3,or(and(X3,or(X,neg(X))),neg(X3)))),
inference(congruence,[status(thm)],[c1223]) ).
cnf(c1225,plain,
f(neg(X),X) = or(X,neg(X)),
inference(substitution,[status(thm)],[c129]) ).
cnf(c1226,plain,
or(X,neg(X)) = f(neg(X),X),
inference(symmetry,[status(thm)],[c1225]) ).
cnf(c1227,plain,
and(X,or(X2,neg(X2))) = and(X,f(neg(X2),X2)),
inference(congruence,[status(thm)],[c1226]) ).
cnf(c1228,plain,
or(and(X2,or(X3,neg(X3))),neg(X)) = or(and(X2,f(neg(X3),X3)),neg(X)),
inference(congruence,[status(thm)],[c1227]) ).
cnf(c1229,plain,
and(X2,or(and(X2,or(X3,neg(X3))),neg(X))) = and(X2,or(and(X2,f(neg(X3),X3)),neg(X))),
inference(congruence,[status(thm)],[c1228]) ).
cnf(c1230,plain,
or(and(or(and(X4,X3),and(X3,X2)),X),and(X3,or(and(X3,or(X4,neg(X4))),neg(X2)))) = or(and(or(and(X4,X3),and(X3,X2)),X),and(X3,or(and(X3,f(neg(X4),X4)),neg(X2)))),
inference(congruence,[status(thm)],[c1229]) ).
cnf(c1231,plain,
neg(f(X,f(neg(X2),X2))) = and(X,f(neg(X2),X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1232,plain,
and(X,f(neg(X2),X2)) = neg(f(X,f(neg(X2),X2))),
inference(symmetry,[status(thm)],[c1231]) ).
cnf(c1233,plain,
or(and(X2,f(neg(X3),X3)),neg(X)) = or(neg(f(X2,f(neg(X3),X3))),neg(X)),
inference(congruence,[status(thm)],[c1232]) ).
cnf(c1234,plain,
and(X2,or(and(X2,f(neg(X3),X3)),neg(X))) = and(X2,or(neg(f(X2,f(neg(X3),X3))),neg(X))),
inference(congruence,[status(thm)],[c1233]) ).
cnf(c1235,plain,
or(and(or(and(X4,X3),and(X3,X2)),X),and(X3,or(and(X3,f(neg(X4),X4)),neg(X2)))) = or(and(or(and(X4,X3),and(X3,X2)),X),and(X3,or(neg(f(X3,f(neg(X4),X4))),neg(X2)))),
inference(congruence,[status(thm)],[c1234]) ).
cnf(c1236,plain,
f(f(X2,f(neg(X3),X3)),X) = or(neg(f(X2,f(neg(X3),X3))),neg(X)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1237,plain,
or(neg(f(X2,f(neg(X3),X3))),neg(X)) = f(f(X2,f(neg(X3),X3)),X),
inference(symmetry,[status(thm)],[c1236]) ).
cnf(c1238,plain,
and(X2,or(neg(f(X2,f(neg(X3),X3))),neg(X))) = and(X2,f(f(X2,f(neg(X3),X3)),X)),
inference(congruence,[status(thm)],[c1237]) ).
cnf(c1239,plain,
or(and(or(and(X4,X3),and(X3,X2)),X),and(X3,or(neg(f(X3,f(neg(X4),X4))),neg(X2)))) = or(and(or(and(X4,X3),and(X3,X2)),X),and(X3,f(f(X3,f(neg(X4),X4)),X2))),
inference(congruence,[status(thm)],[c1238]) ).
cnf(c1240,plain,
neg(f(X2,f(f(X2,f(neg(X3),X3)),X))) = and(X2,f(f(X2,f(neg(X3),X3)),X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1241,plain,
and(X2,f(f(X2,f(neg(X3),X3)),X)) = neg(f(X2,f(f(X2,f(neg(X3),X3)),X))),
inference(symmetry,[status(thm)],[c1240]) ).
cnf(c1242,plain,
or(and(or(and(X4,X3),and(X3,X2)),X),and(X3,f(f(X3,f(neg(X4),X4)),X2))) = or(and(or(and(X4,X3),and(X3,X2)),X),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))),
inference(congruence,[status(thm)],[c1241]) ).
cnf(c1243,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1244,plain,
or(and(X3,X2),and(X2,X)) = or(and(X3,X2),neg(f(X2,X))),
inference(congruence,[status(thm)],[c1243]) ).
cnf(c1245,plain,
and(or(and(X4,X3),and(X3,X2)),X) = and(or(and(X4,X3),neg(f(X3,X2))),X),
inference(congruence,[status(thm)],[c1244]) ).
cnf(c1246,plain,
or(and(or(and(X4,X3),and(X3,X2)),X),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))) = or(and(or(and(X4,X3),neg(f(X3,X2))),X),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))),
inference(congruence,[status(thm)],[c1245]) ).
cnf(c1247,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1248,plain,
or(and(X3,X2),neg(f(X2,X))) = or(neg(f(X3,X2)),neg(f(X2,X))),
inference(congruence,[status(thm)],[c1247]) ).
cnf(c1249,plain,
and(or(and(X4,X3),neg(f(X3,X2))),X) = and(or(neg(f(X4,X3)),neg(f(X3,X2))),X),
inference(congruence,[status(thm)],[c1248]) ).
cnf(c1250,plain,
or(and(or(and(X4,X3),neg(f(X3,X2))),X),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))) = or(and(or(neg(f(X4,X3)),neg(f(X3,X2))),X),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))),
inference(congruence,[status(thm)],[c1249]) ).
cnf(c1251,plain,
f(f(X3,X2),f(X2,X)) = or(neg(f(X3,X2)),neg(f(X2,X))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1252,plain,
or(neg(f(X3,X2)),neg(f(X2,X))) = f(f(X3,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c1251]) ).
cnf(c1253,plain,
and(or(neg(f(X4,X3)),neg(f(X3,X2))),X) = and(f(f(X4,X3),f(X3,X2)),X),
inference(congruence,[status(thm)],[c1252]) ).
cnf(c1254,plain,
or(and(or(neg(f(X4,X3)),neg(f(X3,X2))),X),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))) = or(and(f(f(X4,X3),f(X3,X2)),X),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))),
inference(congruence,[status(thm)],[c1253]) ).
cnf(c1255,plain,
neg(f(f(f(X4,X3),f(X3,X2)),X)) = and(f(f(X4,X3),f(X3,X2)),X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1256,plain,
and(f(f(X4,X3),f(X3,X2)),X) = neg(f(f(f(X4,X3),f(X3,X2)),X)),
inference(symmetry,[status(thm)],[c1255]) ).
cnf(c1257,plain,
or(and(f(f(X4,X3),f(X3,X2)),X),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))) = or(neg(f(f(f(X4,X3),f(X3,X2)),X)),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))),
inference(congruence,[status(thm)],[c1256]) ).
cnf(c1258,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(neg(X4),X4)),X2))) = or(neg(f(f(f(X4,X3),f(X3,X2)),X)),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1259,plain,
or(neg(f(f(f(X4,X3),f(X3,X2)),X)),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))) = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(neg(X4),X4)),X2))),
inference(symmetry,[status(thm)],[c1258]) ).
cnf(c1260,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1261,plain,
f(neg(X),X) = f(f(X,X),X),
inference(congruence,[status(thm)],[c1260]) ).
cnf(c1262,plain,
f(X,f(neg(X2),X2)) = f(X,f(f(X2,X2),X2)),
inference(congruence,[status(thm)],[c1261]) ).
cnf(c1263,plain,
f(f(X2,f(neg(X3),X3)),X) = f(f(X2,f(f(X3,X3),X3)),X),
inference(congruence,[status(thm)],[c1262]) ).
cnf(c1264,plain,
f(X2,f(f(X2,f(neg(X3),X3)),X)) = f(X2,f(f(X2,f(f(X3,X3),X3)),X)),
inference(congruence,[status(thm)],[c1263]) ).
cnf(c1265,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(neg(X4),X4)),X2))) = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))),
inference(congruence,[status(thm)],[c1264]) ).
cnf(c1266,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))) = X3,
inference(substitution,[status(thm)],[c31]) ).
cnf(c1267,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(neg(X4),X4)),X2))) = X3,
inference(transitivity,[status(thm)],[c1265,c1266]) ).
cnf(c1268,plain,
or(neg(f(f(f(X4,X3),f(X3,X2)),X)),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))) = X3,
inference(transitivity,[status(thm)],[c1259,c1267]) ).
cnf(c1269,plain,
or(and(f(f(X4,X3),f(X3,X2)),X),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))) = X3,
inference(transitivity,[status(thm)],[c1257,c1268]) ).
cnf(c1270,plain,
or(and(or(neg(f(X4,X3)),neg(f(X3,X2))),X),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))) = X3,
inference(transitivity,[status(thm)],[c1254,c1269]) ).
cnf(c1271,plain,
or(and(or(and(X4,X3),neg(f(X3,X2))),X),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))) = X3,
inference(transitivity,[status(thm)],[c1250,c1270]) ).
cnf(c1272,plain,
or(and(or(and(X4,X3),and(X3,X2)),X),neg(f(X3,f(f(X3,f(neg(X4),X4)),X2)))) = X3,
inference(transitivity,[status(thm)],[c1246,c1271]) ).
cnf(c1273,plain,
or(and(or(and(X4,X3),and(X3,X2)),X),and(X3,f(f(X3,f(neg(X4),X4)),X2))) = X3,
inference(transitivity,[status(thm)],[c1242,c1272]) ).
cnf(c1274,plain,
or(and(or(and(X4,X3),and(X3,X2)),X),and(X3,or(neg(f(X3,f(neg(X4),X4))),neg(X2)))) = X3,
inference(transitivity,[status(thm)],[c1239,c1273]) ).
cnf(c1275,plain,
or(and(or(and(X4,X3),and(X3,X2)),X),and(X3,or(and(X3,f(neg(X4),X4)),neg(X2)))) = X3,
inference(transitivity,[status(thm)],[c1235,c1274]) ).
cnf(c1276,plain,
or(and(or(and(X4,X3),and(X3,X2)),X),and(X3,or(and(X3,or(X4,neg(X4))),neg(X2)))) = X3,
inference(transitivity,[status(thm)],[c1230,c1275]) ).
cnf(c1277,plain,
or(and(or(and(X,X3),and(X3,X3)),X2),and(X3,or(and(X3,or(X,neg(X))),neg(X3)))) = X3,
inference(substitution,[status(thm)],[c1276]) ).
cnf(c1278,plain,
or(and(or(and(X,X3),X3),X2),and(X3,or(and(X3,or(X,neg(X))),neg(X3)))) = X3,
inference(transitivity,[status(thm)],[c1224,c1277]) ).
cnf(c1279,plain,
or(and(X3,X2),and(X3,or(and(X3,or(X,neg(X))),neg(X3)))) = X3,
inference(transitivity,[status(thm)],[c1213,c1278]) ).
cnf(c1280,plain,
or(and(X3,X2),and(X3,or(neg(X3),and(X3,or(X,neg(X)))))) = X3,
inference(transitivity,[status(thm)],[c1125,c1279]) ).
cnf(c1281,plain,
or(and(X2,or(neg(X2),and(X2,or(X,neg(X))))),and(X2,or(neg(X2),and(X2,or(X,neg(X)))))) = X2,
inference(substitution,[status(thm)],[c1280]) ).
cnf(c1282,plain,
and(X2,or(neg(X2),and(X2,or(X,neg(X))))) = X2,
inference(transitivity,[status(thm)],[c1122,c1281]) ).
cnf(c1283,plain,
X2 = and(X2,or(neg(X2),and(X2,or(X,neg(X))))),
inference(symmetry,[status(thm)],[c1282]) ).
cnf(c1284,plain,
or(and(X2,neg(X2)),X3) = or(and(X2,neg(X2)),and(X3,or(neg(X3),and(X3,or(X,neg(X)))))),
inference(congruence,[status(thm)],[c1283]) ).
cnf(c1285,plain,
and(X2,and(X,neg(X))) = and(and(X,neg(X)),X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c1286,plain,
or(and(X2,and(X,neg(X))),and(or(X,neg(X)),and(X,neg(X)))) = or(and(and(X,neg(X)),X2),and(or(X,neg(X)),and(X,neg(X)))),
inference(congruence,[status(thm)],[c1285]) ).
cnf(c1287,plain,
and(or(X,neg(X)),and(X,neg(X))) = and(and(X,neg(X)),or(X,neg(X))),
inference(substitution,[status(thm)],[c934]) ).
cnf(c1288,plain,
or(and(and(X,neg(X)),X2),and(or(X,neg(X)),and(X,neg(X)))) = or(and(and(X,neg(X)),X2),and(and(X,neg(X)),or(X,neg(X)))),
inference(congruence,[status(thm)],[c1287]) ).
cnf(c1289,plain,
and(neg(X),X) = and(X,neg(X)),
inference(substitution,[status(thm)],[c930]) ).
cnf(c1290,plain,
and(X,neg(X)) = and(neg(X),X),
inference(symmetry,[status(thm)],[c1289]) ).
cnf(c1291,plain,
and(and(X,neg(X)),X2) = and(and(neg(X),X),X2),
inference(congruence,[status(thm)],[c1290]) ).
cnf(c1292,plain,
or(and(and(X,neg(X)),X2),and(and(X,neg(X)),or(X,neg(X)))) = or(and(and(neg(X),X),X2),and(and(X,neg(X)),or(X,neg(X)))),
inference(congruence,[status(thm)],[c1291]) ).
cnf(c1293,plain,
and(neg(X),X) = and(X,neg(X)),
inference(substitution,[status(thm)],[c930]) ).
cnf(c1294,plain,
and(X,neg(X)) = and(neg(X),X),
inference(symmetry,[status(thm)],[c1293]) ).
cnf(c1295,plain,
and(and(X,neg(X)),or(X,neg(X))) = and(and(neg(X),X),or(X,neg(X))),
inference(congruence,[status(thm)],[c1294]) ).
cnf(c1296,plain,
or(and(and(neg(X),X),X2),and(and(X,neg(X)),or(X,neg(X)))) = or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(X)))),
inference(congruence,[status(thm)],[c1295]) ).
cnf(c1297,plain,
and(X2,X) = and(X,X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c1298,plain,
or(and(X3,X2),and(X3,X)) = or(and(X3,X2),and(X,X3)),
inference(congruence,[status(thm)],[c1297]) ).
cnf(c1299,plain,
and(X3,or(and(X3,X2),and(X3,X))) = and(X3,or(and(X3,X2),and(X,X3))),
inference(congruence,[status(thm)],[c1298]) ).
cnf(c1300,plain,
or(neg(X2),neg(X)) = f(X2,X),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c1301,plain,
or(and(X2,X),or(neg(X2),neg(X))) = or(and(X2,X),f(X2,X)),
inference(congruence,[status(thm)],[c1300]) ).
cnf(c1302,plain,
and(X2,or(and(X2,X),or(neg(X2),neg(X)))) = and(X2,or(and(X2,X),f(X2,X))),
inference(congruence,[status(thm)],[c1301]) ).
cnf(c1303,plain,
or(and(X2,X),and(X2,or(and(X2,X),or(neg(X2),neg(X))))) = or(and(X2,X),and(X2,or(and(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c1302]) ).
cnf(c1304,plain,
f(X2,X) = neg(and(X2,X)),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c1305,plain,
or(and(X2,X),f(X2,X)) = or(and(X2,X),neg(and(X2,X))),
inference(congruence,[status(thm)],[c1304]) ).
cnf(c1306,plain,
and(X2,or(and(X2,X),f(X2,X))) = and(X2,or(and(X2,X),neg(and(X2,X)))),
inference(congruence,[status(thm)],[c1305]) ).
cnf(c1307,plain,
or(and(X2,X),and(X2,or(and(X2,X),f(X2,X)))) = or(and(X2,X),and(X2,or(and(X2,X),neg(and(X2,X))))),
inference(congruence,[status(thm)],[c1306]) ).
cnf(c1308,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1309,plain,
and(X2,X) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c1308]) ).
cnf(c1310,plain,
or(and(X2,X),neg(and(X2,X))) = or(and(X2,neg(neg(X))),neg(and(X2,X))),
inference(congruence,[status(thm)],[c1309]) ).
cnf(c1311,plain,
and(X2,or(and(X2,X),neg(and(X2,X)))) = and(X2,or(and(X2,neg(neg(X))),neg(and(X2,X)))),
inference(congruence,[status(thm)],[c1310]) ).
cnf(c1312,plain,
or(and(X2,X),and(X2,or(and(X2,X),neg(and(X2,X))))) = or(and(X2,X),and(X2,or(and(X2,neg(neg(X))),neg(and(X2,X))))),
inference(congruence,[status(thm)],[c1311]) ).
cnf(c1313,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1314,plain,
and(X2,neg(neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(congruence,[status(thm)],[c1313]) ).
cnf(c1315,plain,
or(and(X2,neg(neg(X))),neg(and(X2,X))) = or(and(neg(neg(X2)),neg(neg(X))),neg(and(X2,X))),
inference(congruence,[status(thm)],[c1314]) ).
cnf(c1316,plain,
and(X2,or(and(X2,neg(neg(X))),neg(and(X2,X)))) = and(X2,or(and(neg(neg(X2)),neg(neg(X))),neg(and(X2,X)))),
inference(congruence,[status(thm)],[c1315]) ).
cnf(c1317,plain,
or(and(X2,X),and(X2,or(and(X2,neg(neg(X))),neg(and(X2,X))))) = or(and(X2,X),and(X2,or(and(neg(neg(X2)),neg(neg(X))),neg(and(X2,X))))),
inference(congruence,[status(thm)],[c1316]) ).
cnf(c1318,plain,
neg(or(neg(X2),neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1319,plain,
and(neg(neg(X2)),neg(neg(X))) = neg(or(neg(X2),neg(X))),
inference(symmetry,[status(thm)],[c1318]) ).
cnf(c1320,plain,
or(and(neg(neg(X2)),neg(neg(X))),neg(and(X2,X))) = or(neg(or(neg(X2),neg(X))),neg(and(X2,X))),
inference(congruence,[status(thm)],[c1319]) ).
cnf(c1321,plain,
and(X2,or(and(neg(neg(X2)),neg(neg(X))),neg(and(X2,X)))) = and(X2,or(neg(or(neg(X2),neg(X))),neg(and(X2,X)))),
inference(congruence,[status(thm)],[c1320]) ).
cnf(c1322,plain,
or(and(X2,X),and(X2,or(and(neg(neg(X2)),neg(neg(X))),neg(and(X2,X))))) = or(and(X2,X),and(X2,or(neg(or(neg(X2),neg(X))),neg(and(X2,X))))),
inference(congruence,[status(thm)],[c1321]) ).
cnf(c1323,plain,
f(or(neg(X2),neg(X)),and(X2,X)) = or(neg(or(neg(X2),neg(X))),neg(and(X2,X))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1324,plain,
or(neg(or(neg(X2),neg(X))),neg(and(X2,X))) = f(or(neg(X2),neg(X)),and(X2,X)),
inference(symmetry,[status(thm)],[c1323]) ).
cnf(c1325,plain,
and(X2,or(neg(or(neg(X2),neg(X))),neg(and(X2,X)))) = and(X2,f(or(neg(X2),neg(X)),and(X2,X))),
inference(congruence,[status(thm)],[c1324]) ).
cnf(c1326,plain,
or(and(X2,X),and(X2,or(neg(or(neg(X2),neg(X))),neg(and(X2,X))))) = or(and(X2,X),and(X2,f(or(neg(X2),neg(X)),and(X2,X)))),
inference(congruence,[status(thm)],[c1325]) ).
cnf(c1327,plain,
neg(and(or(neg(X2),neg(X)),and(X2,X))) = f(or(neg(X2),neg(X)),and(X2,X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1328,plain,
f(or(neg(X2),neg(X)),and(X2,X)) = neg(and(or(neg(X2),neg(X)),and(X2,X))),
inference(symmetry,[status(thm)],[c1327]) ).
cnf(c1329,plain,
and(X2,f(or(neg(X2),neg(X)),and(X2,X))) = and(X2,neg(and(or(neg(X2),neg(X)),and(X2,X)))),
inference(congruence,[status(thm)],[c1328]) ).
cnf(c1330,plain,
or(and(X2,X),and(X2,f(or(neg(X2),neg(X)),and(X2,X)))) = or(and(X2,X),and(X2,neg(and(or(neg(X2),neg(X)),and(X2,X))))),
inference(congruence,[status(thm)],[c1329]) ).
cnf(c1331,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1332,plain,
and(X2,neg(and(or(neg(X2),neg(X)),and(X2,X)))) = and(neg(neg(X2)),neg(and(or(neg(X2),neg(X)),and(X2,X)))),
inference(congruence,[status(thm)],[c1331]) ).
cnf(c1333,plain,
or(and(X2,X),and(X2,neg(and(or(neg(X2),neg(X)),and(X2,X))))) = or(and(X2,X),and(neg(neg(X2)),neg(and(or(neg(X2),neg(X)),and(X2,X))))),
inference(congruence,[status(thm)],[c1332]) ).
cnf(c1334,plain,
neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X)))) = and(neg(neg(X2)),neg(and(or(neg(X2),neg(X)),and(X2,X)))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1335,plain,
and(neg(neg(X2)),neg(and(or(neg(X2),neg(X)),and(X2,X)))) = neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X)))),
inference(symmetry,[status(thm)],[c1334]) ).
cnf(c1336,plain,
or(and(X2,X),and(neg(neg(X2)),neg(and(or(neg(X2),neg(X)),and(X2,X))))) = or(and(X2,X),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))),
inference(congruence,[status(thm)],[c1335]) ).
cnf(c1337,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1338,plain,
and(X2,X) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c1337]) ).
cnf(c1339,plain,
or(and(X2,X),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))) = or(and(X2,neg(neg(X))),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))),
inference(congruence,[status(thm)],[c1338]) ).
cnf(c1340,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1341,plain,
and(X2,neg(neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(congruence,[status(thm)],[c1340]) ).
cnf(c1342,plain,
or(and(X2,neg(neg(X))),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))) = or(and(neg(neg(X2)),neg(neg(X))),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))),
inference(congruence,[status(thm)],[c1341]) ).
cnf(c1343,plain,
neg(or(neg(X2),neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1344,plain,
and(neg(neg(X2)),neg(neg(X))) = neg(or(neg(X2),neg(X))),
inference(symmetry,[status(thm)],[c1343]) ).
cnf(c1345,plain,
or(and(neg(neg(X2)),neg(neg(X))),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))) = or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))),
inference(congruence,[status(thm)],[c1344]) ).
cnf(c1346,plain,
f(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X)))) = or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1347,plain,
or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))) = f(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X)))),
inference(symmetry,[status(thm)],[c1346]) ).
cnf(c1348,plain,
neg(and(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))) = f(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X)))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1349,plain,
f(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X)))) = neg(and(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))),
inference(symmetry,[status(thm)],[c1348]) ).
cnf(c1350,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1351,plain,
and(X2,X) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c1350]) ).
cnf(c1352,plain,
and(or(neg(X2),neg(X)),and(X2,X)) = and(or(neg(X2),neg(X)),and(X2,neg(neg(X)))),
inference(congruence,[status(thm)],[c1351]) ).
cnf(c1353,plain,
or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))) = or(neg(X2),and(or(neg(X2),neg(X)),and(X2,neg(neg(X))))),
inference(congruence,[status(thm)],[c1352]) ).
cnf(c1354,plain,
and(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X)))) = and(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,neg(neg(X)))))),
inference(congruence,[status(thm)],[c1353]) ).
cnf(c1355,plain,
and(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,neg(neg(X)))))) = neg(X2),
inference(substitution,[status(thm)],[c353]) ).
cnf(c1356,plain,
and(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X)))) = neg(X2),
inference(transitivity,[status(thm)],[c1354,c1355]) ).
cnf(c1357,plain,
neg(and(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))) = neg(neg(X2)),
inference(congruence,[status(thm)],[c1356]) ).
cnf(c1358,plain,
neg(and(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c1357,c79]) ).
cnf(c1359,plain,
f(or(neg(X2),neg(X)),or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X)))) = X2,
inference(transitivity,[status(thm)],[c1349,c1358]) ).
cnf(c1360,plain,
or(neg(or(neg(X2),neg(X))),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c1347,c1359]) ).
cnf(c1361,plain,
or(and(neg(neg(X2)),neg(neg(X))),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c1345,c1360]) ).
cnf(c1362,plain,
or(and(X2,neg(neg(X))),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c1342,c1361]) ).
cnf(c1363,plain,
or(and(X2,X),neg(or(neg(X2),and(or(neg(X2),neg(X)),and(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c1339,c1362]) ).
cnf(c1364,plain,
or(and(X2,X),and(neg(neg(X2)),neg(and(or(neg(X2),neg(X)),and(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c1336,c1363]) ).
cnf(c1365,plain,
or(and(X2,X),and(X2,neg(and(or(neg(X2),neg(X)),and(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c1333,c1364]) ).
cnf(c1366,plain,
or(and(X2,X),and(X2,f(or(neg(X2),neg(X)),and(X2,X)))) = X2,
inference(transitivity,[status(thm)],[c1330,c1365]) ).
cnf(c1367,plain,
or(and(X2,X),and(X2,or(neg(or(neg(X2),neg(X))),neg(and(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c1326,c1366]) ).
cnf(c1368,plain,
or(and(X2,X),and(X2,or(and(neg(neg(X2)),neg(neg(X))),neg(and(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c1322,c1367]) ).
cnf(c1369,plain,
or(and(X2,X),and(X2,or(and(X2,neg(neg(X))),neg(and(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c1317,c1368]) ).
cnf(c1370,plain,
or(and(X2,X),and(X2,or(and(X2,X),neg(and(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c1312,c1369]) ).
cnf(c1371,plain,
or(and(X2,X),and(X2,or(and(X2,X),f(X2,X)))) = X2,
inference(transitivity,[status(thm)],[c1307,c1370]) ).
cnf(c1372,plain,
or(and(X2,X),and(X2,or(and(X2,X),or(neg(X2),neg(X))))) = X2,
inference(transitivity,[status(thm)],[c1303,c1371]) ).
cnf(c1373,plain,
X2 = or(and(X2,X),and(X2,or(and(X2,X),or(neg(X2),neg(X))))),
inference(symmetry,[status(thm)],[c1372]) ).
cnf(c1374,plain,
and(X,X3) = and(X,or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2)))))),
inference(congruence,[status(thm)],[c1373]) ).
cnf(c1375,plain,
or(and(X3,X2),and(X,X3)) = or(and(X3,X2),and(X,or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2))))))),
inference(congruence,[status(thm)],[c1374]) ).
cnf(c1376,plain,
and(X3,or(and(X3,X2),and(X,X3))) = and(X3,or(and(X3,X2),and(X,or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2)))))))),
inference(congruence,[status(thm)],[c1375]) ).
cnf(c1377,plain,
X2 = or(and(X2,X),and(X2,or(and(X2,X),or(neg(X2),neg(X))))),
inference(symmetry,[status(thm)],[c1372]) ).
cnf(c1378,plain,
and(X3,or(and(X3,X2),and(X,or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2)))))))) = and(or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2))))),or(and(X3,X2),and(X,or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2)))))))),
inference(congruence,[status(thm)],[c1377]) ).
cnf(c1379,plain,
or(X3,and(X,or(X3,X2))) = or(and(X,or(X3,X2)),X3),
inference(substitution,[status(thm)],[c913]) ).
cnf(c1380,plain,
and(or(X3,X2),or(X3,and(X,or(X3,X2)))) = and(or(X3,X2),or(and(X,or(X3,X2)),X3)),
inference(congruence,[status(thm)],[c1379]) ).
cnf(c1381,plain,
X2 = and(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X))))),
inference(symmetry,[status(thm)],[c358]) ).
cnf(c1382,plain,
or(and(X,or(X3,X2)),X3) = or(and(X,or(X3,X2)),and(or(X3,X2),or(X3,and(or(X3,X2),and(neg(X3),neg(X2)))))),
inference(congruence,[status(thm)],[c1381]) ).
cnf(c1383,plain,
and(or(X3,X2),or(and(X,or(X3,X2)),X3)) = and(or(X3,X2),or(and(X,or(X3,X2)),and(or(X3,X2),or(X3,and(or(X3,X2),and(neg(X3),neg(X2))))))),
inference(congruence,[status(thm)],[c1382]) ).
cnf(c1384,plain,
and(or(X3,X2),or(and(X,or(X3,X2)),and(or(X3,X2),or(X3,and(or(X3,X2),and(neg(X3),neg(X2))))))) = or(and(X,or(X3,X2)),and(or(X3,X2),or(X3,and(or(X3,X2),and(neg(X3),neg(X2)))))),
inference(substitution,[status(thm)],[c527]) ).
cnf(c1385,plain,
or(and(X,or(X3,X2)),and(or(X3,X2),or(X3,and(or(X3,X2),and(neg(X3),neg(X2)))))) = or(and(X,or(X3,X2)),X3),
inference(congruence,[status(thm)],[c358]) ).
cnf(c1386,plain,
or(X3,and(X,or(X3,X2))) = or(and(X,or(X3,X2)),X3),
inference(substitution,[status(thm)],[c913]) ).
cnf(c1387,plain,
or(and(X,or(X3,X2)),X3) = or(X3,and(X,or(X3,X2))),
inference(symmetry,[status(thm)],[c1386]) ).
cnf(c1388,plain,
or(and(X,or(X3,X2)),and(or(X3,X2),or(X3,and(or(X3,X2),and(neg(X3),neg(X2)))))) = or(X3,and(X,or(X3,X2))),
inference(transitivity,[status(thm)],[c1385,c1387]) ).
cnf(c1389,plain,
and(or(X3,X2),or(and(X,or(X3,X2)),and(or(X3,X2),or(X3,and(or(X3,X2),and(neg(X3),neg(X2))))))) = or(X3,and(X,or(X3,X2))),
inference(transitivity,[status(thm)],[c1384,c1388]) ).
cnf(c1390,plain,
and(or(X3,X2),or(and(X,or(X3,X2)),X3)) = or(X3,and(X,or(X3,X2))),
inference(transitivity,[status(thm)],[c1383,c1389]) ).
cnf(c1391,plain,
and(or(X3,X2),or(X3,and(X,or(X3,X2)))) = or(X3,and(X,or(X3,X2))),
inference(transitivity,[status(thm)],[c1380,c1390]) ).
cnf(c1392,plain,
and(or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2))))),or(and(X3,X2),and(X,or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2)))))))) = or(and(X3,X2),and(X,or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2))))))),
inference(substitution,[status(thm)],[c1391]) ).
cnf(c1393,plain,
and(X,or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2)))))) = and(X,X3),
inference(congruence,[status(thm)],[c1372]) ).
cnf(c1394,plain,
or(and(X3,X2),and(X,or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2))))))) = or(and(X3,X2),and(X,X3)),
inference(congruence,[status(thm)],[c1393]) ).
cnf(c1395,plain,
and(X2,X) = and(X,X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c1396,plain,
and(X,X2) = and(X2,X),
inference(symmetry,[status(thm)],[c1395]) ).
cnf(c1397,plain,
or(and(X3,X2),and(X,X3)) = or(and(X3,X2),and(X3,X)),
inference(congruence,[status(thm)],[c1396]) ).
cnf(c1398,plain,
or(and(X3,X2),and(X,or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2))))))) = or(and(X3,X2),and(X3,X)),
inference(transitivity,[status(thm)],[c1394,c1397]) ).
cnf(c1399,plain,
and(or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2))))),or(and(X3,X2),and(X,or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2)))))))) = or(and(X3,X2),and(X3,X)),
inference(transitivity,[status(thm)],[c1392,c1398]) ).
cnf(c1400,plain,
and(X3,or(and(X3,X2),and(X,or(and(X3,X2),and(X3,or(and(X3,X2),or(neg(X3),neg(X2)))))))) = or(and(X3,X2),and(X3,X)),
inference(transitivity,[status(thm)],[c1378,c1399]) ).
cnf(c1401,plain,
and(X3,or(and(X3,X2),and(X,X3))) = or(and(X3,X2),and(X3,X)),
inference(transitivity,[status(thm)],[c1376,c1400]) ).
cnf(c1402,plain,
and(X3,or(and(X3,X2),and(X3,X))) = or(and(X3,X2),and(X3,X)),
inference(transitivity,[status(thm)],[c1299,c1401]) ).
cnf(c1403,plain,
and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(X))))) = or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(X)))),
inference(substitution,[status(thm)],[c1402]) ).
cnf(c1404,plain,
or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(X)))) = and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(X))))),
inference(symmetry,[status(thm)],[c1403]) ).
cnf(c1405,plain,
neg(neg(or(X,neg(X)))) = or(X,neg(X)),
inference(substitution,[status(thm)],[c79]) ).
cnf(c1406,plain,
or(X,neg(X)) = neg(neg(or(X,neg(X)))),
inference(symmetry,[status(thm)],[c1405]) ).
cnf(c1407,plain,
or(X,or(X,neg(X))) = or(X,neg(neg(or(X,neg(X))))),
inference(congruence,[status(thm)],[c1406]) ).
cnf(c1408,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1409,plain,
or(X,neg(neg(or(X,neg(X))))) = or(neg(neg(X)),neg(neg(or(X,neg(X))))),
inference(congruence,[status(thm)],[c1408]) ).
cnf(c1410,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1411,plain,
or(X,neg(X)) = or(neg(neg(X)),neg(X)),
inference(congruence,[status(thm)],[c1410]) ).
cnf(c1412,plain,
neg(or(X,neg(X))) = neg(or(neg(neg(X)),neg(X))),
inference(congruence,[status(thm)],[c1411]) ).
cnf(c1413,plain,
neg(neg(or(X,neg(X)))) = neg(neg(or(neg(neg(X)),neg(X)))),
inference(congruence,[status(thm)],[c1412]) ).
cnf(c1414,plain,
or(neg(neg(X)),neg(neg(or(X,neg(X))))) = or(neg(neg(X)),neg(neg(or(neg(neg(X)),neg(X))))),
inference(congruence,[status(thm)],[c1413]) ).
cnf(c1415,plain,
and(or(neg(neg(X)),neg(X)),or(neg(neg(X)),neg(X))) = neg(neg(or(neg(neg(X)),neg(X)))),
inference(substitution,[status(thm)],[c122]) ).
cnf(c1416,plain,
neg(neg(or(neg(neg(X)),neg(X)))) = and(or(neg(neg(X)),neg(X)),or(neg(neg(X)),neg(X))),
inference(symmetry,[status(thm)],[c1415]) ).
cnf(c1417,plain,
or(neg(neg(X)),neg(neg(or(neg(neg(X)),neg(X))))) = or(neg(neg(X)),and(or(neg(neg(X)),neg(X)),or(neg(neg(X)),neg(X)))),
inference(congruence,[status(thm)],[c1416]) ).
cnf(c1418,plain,
or(neg(neg(X)),and(or(neg(neg(X)),neg(X)),or(neg(neg(X)),neg(X)))) = or(neg(neg(X)),neg(X)),
inference(substitution,[status(thm)],[c332]) ).
cnf(c1419,plain,
or(neg(neg(X)),neg(X)) = or(X,neg(X)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c1420,plain,
or(neg(neg(X)),and(or(neg(neg(X)),neg(X)),or(neg(neg(X)),neg(X)))) = or(X,neg(X)),
inference(transitivity,[status(thm)],[c1418,c1419]) ).
cnf(c1421,plain,
or(neg(neg(X)),neg(neg(or(neg(neg(X)),neg(X))))) = or(X,neg(X)),
inference(transitivity,[status(thm)],[c1417,c1420]) ).
cnf(c1422,plain,
or(neg(neg(X)),neg(neg(or(X,neg(X))))) = or(X,neg(X)),
inference(transitivity,[status(thm)],[c1414,c1421]) ).
cnf(c1423,plain,
or(X,neg(neg(or(X,neg(X))))) = or(X,neg(X)),
inference(transitivity,[status(thm)],[c1409,c1422]) ).
cnf(c1424,plain,
or(X,or(X,neg(X))) = or(X,neg(X)),
inference(transitivity,[status(thm)],[c1407,c1423]) ).
cnf(c1425,plain,
or(X,neg(X)) = or(X,or(X,neg(X))),
inference(symmetry,[status(thm)],[c1424]) ).
cnf(c1426,plain,
and(and(neg(X),X),or(X,neg(X))) = and(and(neg(X),X),or(X,or(X,neg(X)))),
inference(congruence,[status(thm)],[c1425]) ).
cnf(c1427,plain,
or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(X)))) = or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,or(X,neg(X))))),
inference(congruence,[status(thm)],[c1426]) ).
cnf(c1428,plain,
and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(X))))) = and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,or(X,neg(X)))))),
inference(congruence,[status(thm)],[c1427]) ).
cnf(c1429,plain,
f(neg(X),X) = or(X,neg(X)),
inference(substitution,[status(thm)],[c129]) ).
cnf(c1430,plain,
or(X,neg(X)) = f(neg(X),X),
inference(symmetry,[status(thm)],[c1429]) ).
cnf(c1431,plain,
or(X,or(X,neg(X))) = or(X,f(neg(X),X)),
inference(congruence,[status(thm)],[c1430]) ).
cnf(c1432,plain,
and(and(neg(X),X),or(X,or(X,neg(X)))) = and(and(neg(X),X),or(X,f(neg(X),X))),
inference(congruence,[status(thm)],[c1431]) ).
cnf(c1433,plain,
or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,or(X,neg(X))))) = or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,f(neg(X),X)))),
inference(congruence,[status(thm)],[c1432]) ).
cnf(c1434,plain,
and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,or(X,neg(X)))))) = and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,f(neg(X),X))))),
inference(congruence,[status(thm)],[c1433]) ).
cnf(c1435,plain,
neg(and(neg(X),X)) = f(neg(X),X),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1436,plain,
f(neg(X),X) = neg(and(neg(X),X)),
inference(symmetry,[status(thm)],[c1435]) ).
cnf(c1437,plain,
or(X,f(neg(X),X)) = or(X,neg(and(neg(X),X))),
inference(congruence,[status(thm)],[c1436]) ).
cnf(c1438,plain,
and(and(neg(X),X),or(X,f(neg(X),X))) = and(and(neg(X),X),or(X,neg(and(neg(X),X)))),
inference(congruence,[status(thm)],[c1437]) ).
cnf(c1439,plain,
or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,f(neg(X),X)))) = or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(and(neg(X),X))))),
inference(congruence,[status(thm)],[c1438]) ).
cnf(c1440,plain,
and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,f(neg(X),X))))) = and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(and(neg(X),X)))))),
inference(congruence,[status(thm)],[c1439]) ).
cnf(c1441,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1442,plain,
or(X,neg(and(neg(X),X))) = or(neg(neg(X)),neg(and(neg(X),X))),
inference(congruence,[status(thm)],[c1441]) ).
cnf(c1443,plain,
and(and(neg(X),X),or(X,neg(and(neg(X),X)))) = and(and(neg(X),X),or(neg(neg(X)),neg(and(neg(X),X)))),
inference(congruence,[status(thm)],[c1442]) ).
cnf(c1444,plain,
or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(and(neg(X),X))))) = or(and(and(neg(X),X),X2),and(and(neg(X),X),or(neg(neg(X)),neg(and(neg(X),X))))),
inference(congruence,[status(thm)],[c1443]) ).
cnf(c1445,plain,
and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(and(neg(X),X)))))) = and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(neg(neg(X)),neg(and(neg(X),X)))))),
inference(congruence,[status(thm)],[c1444]) ).
cnf(c1446,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1447,plain,
or(X2,and(X2,X)) = or(X2,neg(f(X2,X))),
inference(congruence,[status(thm)],[c1446]) ).
cnf(c1448,plain,
and(or(X2,and(X2,X)),X2) = and(or(X2,neg(f(X2,X))),X2),
inference(congruence,[status(thm)],[c1447]) ).
cnf(c1449,plain,
or(X2,and(or(X2,and(X2,X)),X2)) = or(X2,and(or(X2,neg(f(X2,X))),X2)),
inference(congruence,[status(thm)],[c1448]) ).
cnf(c1450,plain,
f(neg(X2),f(X2,X)) = or(X2,neg(f(X2,X))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c1451,plain,
or(X2,neg(f(X2,X))) = f(neg(X2),f(X2,X)),
inference(symmetry,[status(thm)],[c1450]) ).
cnf(c1452,plain,
and(or(X2,neg(f(X2,X))),X2) = and(f(neg(X2),f(X2,X)),X2),
inference(congruence,[status(thm)],[c1451]) ).
cnf(c1453,plain,
or(X2,and(or(X2,neg(f(X2,X))),X2)) = or(X2,and(f(neg(X2),f(X2,X)),X2)),
inference(congruence,[status(thm)],[c1452]) ).
cnf(c1454,plain,
neg(f(f(neg(X2),f(X2,X)),X2)) = and(f(neg(X2),f(X2,X)),X2),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1455,plain,
and(f(neg(X2),f(X2,X)),X2) = neg(f(f(neg(X2),f(X2,X)),X2)),
inference(symmetry,[status(thm)],[c1454]) ).
cnf(c1456,plain,
or(X2,and(f(neg(X2),f(X2,X)),X2)) = or(X2,neg(f(f(neg(X2),f(X2,X)),X2))),
inference(congruence,[status(thm)],[c1455]) ).
cnf(c1457,plain,
f(neg(X2),f(f(neg(X2),f(X2,X)),X2)) = or(X2,neg(f(f(neg(X2),f(X2,X)),X2))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c1458,plain,
or(X2,neg(f(f(neg(X2),f(X2,X)),X2))) = f(neg(X2),f(f(neg(X2),f(X2,X)),X2)),
inference(symmetry,[status(thm)],[c1457]) ).
cnf(c1459,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1460,plain,
f(neg(X2),f(X2,X)) = f(f(X2,X2),f(X2,X)),
inference(congruence,[status(thm)],[c1459]) ).
cnf(c1461,plain,
f(f(neg(X2),f(X2,X)),X2) = f(f(f(X2,X2),f(X2,X)),X2),
inference(congruence,[status(thm)],[c1460]) ).
cnf(c1462,plain,
f(neg(X2),f(f(neg(X2),f(X2,X)),X2)) = f(neg(X2),f(f(f(X2,X2),f(X2,X)),X2)),
inference(congruence,[status(thm)],[c1461]) ).
cnf(c1463,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1464,plain,
f(neg(X2),f(f(f(X2,X2),f(X2,X)),X2)) = f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),X2)),
inference(congruence,[status(thm)],[c1463]) ).
cnf(c1465,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),X2)) = f(f(X2,X2),f(X2,X)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c1466,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1467,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c1466]) ).
cnf(c1468,plain,
f(f(X2,X2),f(X2,X)) = f(neg(X2),f(X2,X)),
inference(congruence,[status(thm)],[c1467]) ).
cnf(c1469,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),X2)) = f(neg(X2),f(X2,X)),
inference(transitivity,[status(thm)],[c1465,c1468]) ).
cnf(c1470,plain,
f(neg(X2),f(f(f(X2,X2),f(X2,X)),X2)) = f(neg(X2),f(X2,X)),
inference(transitivity,[status(thm)],[c1464,c1469]) ).
cnf(c1471,plain,
f(neg(X2),f(f(neg(X2),f(X2,X)),X2)) = f(neg(X2),f(X2,X)),
inference(transitivity,[status(thm)],[c1462,c1470]) ).
cnf(c1472,plain,
f(neg(X2),f(X2,X)) = or(X2,neg(f(X2,X))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c1473,plain,
or(X2,neg(f(X2,X))) = or(X2,and(X2,X)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1474,plain,
f(neg(X2),f(X2,X)) = or(X2,and(X2,X)),
inference(transitivity,[status(thm)],[c1472,c1473]) ).
cnf(c1475,plain,
f(neg(X2),f(f(neg(X2),f(X2,X)),X2)) = or(X2,and(X2,X)),
inference(transitivity,[status(thm)],[c1471,c1474]) ).
cnf(c1476,plain,
or(X2,neg(f(f(neg(X2),f(X2,X)),X2))) = or(X2,and(X2,X)),
inference(transitivity,[status(thm)],[c1458,c1475]) ).
cnf(c1477,plain,
or(X2,and(f(neg(X2),f(X2,X)),X2)) = or(X2,and(X2,X)),
inference(transitivity,[status(thm)],[c1456,c1476]) ).
cnf(c1478,plain,
or(X2,and(or(X2,neg(f(X2,X))),X2)) = or(X2,and(X2,X)),
inference(transitivity,[status(thm)],[c1453,c1477]) ).
cnf(c1479,plain,
or(X2,and(or(X2,and(X2,X)),X2)) = or(X2,and(X2,X)),
inference(transitivity,[status(thm)],[c1449,c1478]) ).
cnf(c1480,plain,
or(X2,and(X2,X)) = or(X2,and(or(X2,and(X2,X)),X2)),
inference(symmetry,[status(thm)],[c1479]) ).
cnf(c1481,plain,
and(or(X2,and(X2,X)),X2) = X2,
inference(substitution,[status(thm)],[c525]) ).
cnf(c1482,plain,
or(X2,and(or(X2,and(X2,X)),X2)) = or(X2,X2),
inference(congruence,[status(thm)],[c1481]) ).
cnf(c1483,plain,
or(X,X) = X,
inference(transitivity,[status(thm)],[c19,c79]) ).
cnf(c1484,plain,
or(X2,and(or(X2,and(X2,X)),X2)) = X2,
inference(transitivity,[status(thm)],[c1482,c1483]) ).
cnf(c1485,plain,
or(X2,and(X2,X)) = X2,
inference(transitivity,[status(thm)],[c1480,c1484]) ).
cnf(c1486,plain,
or(and(neg(X2),X2),and(and(neg(X2),X2),X)) = and(neg(X2),X2),
inference(substitution,[status(thm)],[c1485]) ).
cnf(c1487,plain,
and(neg(X2),X2) = or(and(neg(X2),X2),and(and(neg(X2),X2),X)),
inference(symmetry,[status(thm)],[c1486]) ).
cnf(c1488,plain,
and(and(neg(X2),X2),or(and(and(neg(X2),X2),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(and(neg(X2),X2)))))) = and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),or(and(and(neg(X2),X2),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(and(neg(X2),X2)))))),
inference(congruence,[status(thm)],[c1487]) ).
cnf(c1489,plain,
or(and(neg(X2),X2),and(and(neg(X2),X2),X)) = and(neg(X2),X2),
inference(substitution,[status(thm)],[c1485]) ).
cnf(c1490,plain,
and(neg(X2),X2) = or(and(neg(X2),X2),and(and(neg(X2),X2),X)),
inference(symmetry,[status(thm)],[c1489]) ).
cnf(c1491,plain,
and(and(neg(X2),X2),X3) = and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),
inference(congruence,[status(thm)],[c1490]) ).
cnf(c1492,plain,
or(and(and(neg(X2),X2),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(and(neg(X2),X2))))) = or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(and(neg(X2),X2))))),
inference(congruence,[status(thm)],[c1491]) ).
cnf(c1493,plain,
and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),or(and(and(neg(X2),X2),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(and(neg(X2),X2)))))) = and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(and(neg(X2),X2)))))),
inference(congruence,[status(thm)],[c1492]) ).
cnf(c1494,plain,
or(and(neg(X2),X2),and(and(neg(X2),X2),X)) = and(neg(X2),X2),
inference(substitution,[status(thm)],[c1485]) ).
cnf(c1495,plain,
and(neg(X2),X2) = or(and(neg(X2),X2),and(and(neg(X2),X2),X)),
inference(symmetry,[status(thm)],[c1494]) ).
cnf(c1496,plain,
neg(and(neg(X2),X2)) = neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X))),
inference(congruence,[status(thm)],[c1495]) ).
cnf(c1497,plain,
or(neg(neg(X2)),neg(and(neg(X2),X2))) = or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X)))),
inference(congruence,[status(thm)],[c1496]) ).
cnf(c1498,plain,
and(and(neg(X2),X2),or(neg(neg(X2)),neg(and(neg(X2),X2)))) = and(and(neg(X2),X2),or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X))))),
inference(congruence,[status(thm)],[c1497]) ).
cnf(c1499,plain,
or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(and(neg(X2),X2))))) = or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X)))))),
inference(congruence,[status(thm)],[c1498]) ).
cnf(c1500,plain,
and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(and(neg(X2),X2)))))) = and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X))))))),
inference(congruence,[status(thm)],[c1499]) ).
cnf(c1501,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1502,plain,
and(and(neg(X2),X2),X) = and(and(neg(X2),X2),neg(neg(X))),
inference(congruence,[status(thm)],[c1501]) ).
cnf(c1503,plain,
or(and(neg(X2),X2),and(and(neg(X2),X2),X)) = or(and(neg(X2),X2),and(and(neg(X2),X2),neg(neg(X)))),
inference(congruence,[status(thm)],[c1502]) ).
cnf(c1504,plain,
and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),X2),X))) = and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),X2),neg(neg(X))))),
inference(congruence,[status(thm)],[c1503]) ).
cnf(c1505,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1506,plain,
and(neg(X),X) = and(neg(X),neg(neg(X))),
inference(congruence,[status(thm)],[c1505]) ).
cnf(c1507,plain,
and(and(neg(X2),X2),neg(neg(X))) = and(and(neg(X2),neg(neg(X2))),neg(neg(X))),
inference(congruence,[status(thm)],[c1506]) ).
cnf(c1508,plain,
or(and(neg(X2),X2),and(and(neg(X2),X2),neg(neg(X)))) = or(and(neg(X2),X2),and(and(neg(X2),neg(neg(X2))),neg(neg(X)))),
inference(congruence,[status(thm)],[c1507]) ).
cnf(c1509,plain,
and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),X2),neg(neg(X))))) = and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),neg(neg(X2))),neg(neg(X))))),
inference(congruence,[status(thm)],[c1508]) ).
cnf(c1510,plain,
neg(or(X,neg(X))) = and(neg(X),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1511,plain,
and(neg(X),neg(neg(X))) = neg(or(X,neg(X))),
inference(symmetry,[status(thm)],[c1510]) ).
cnf(c1512,plain,
and(and(neg(X2),neg(neg(X2))),neg(neg(X))) = and(neg(or(X2,neg(X2))),neg(neg(X))),
inference(congruence,[status(thm)],[c1511]) ).
cnf(c1513,plain,
or(and(neg(X2),X2),and(and(neg(X2),neg(neg(X2))),neg(neg(X)))) = or(and(neg(X2),X2),and(neg(or(X2,neg(X2))),neg(neg(X)))),
inference(congruence,[status(thm)],[c1512]) ).
cnf(c1514,plain,
and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),neg(neg(X2))),neg(neg(X))))) = and(neg(X2),or(and(neg(X2),X2),and(neg(or(X2,neg(X2))),neg(neg(X))))),
inference(congruence,[status(thm)],[c1513]) ).
cnf(c1515,plain,
neg(or(or(X2,neg(X2)),neg(X))) = and(neg(or(X2,neg(X2))),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1516,plain,
and(neg(or(X2,neg(X2))),neg(neg(X))) = neg(or(or(X2,neg(X2)),neg(X))),
inference(symmetry,[status(thm)],[c1515]) ).
cnf(c1517,plain,
or(and(neg(X2),X2),and(neg(or(X2,neg(X2))),neg(neg(X)))) = or(and(neg(X2),X2),neg(or(or(X2,neg(X2)),neg(X)))),
inference(congruence,[status(thm)],[c1516]) ).
cnf(c1518,plain,
and(neg(X2),or(and(neg(X2),X2),and(neg(or(X2,neg(X2))),neg(neg(X))))) = and(neg(X2),or(and(neg(X2),X2),neg(or(or(X2,neg(X2)),neg(X))))),
inference(congruence,[status(thm)],[c1517]) ).
cnf(c1519,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1520,plain,
and(neg(X),X) = and(neg(X),neg(neg(X))),
inference(congruence,[status(thm)],[c1519]) ).
cnf(c1521,plain,
or(and(neg(X2),X2),neg(or(or(X2,neg(X2)),neg(X)))) = or(and(neg(X2),neg(neg(X2))),neg(or(or(X2,neg(X2)),neg(X)))),
inference(congruence,[status(thm)],[c1520]) ).
cnf(c1522,plain,
and(neg(X2),or(and(neg(X2),X2),neg(or(or(X2,neg(X2)),neg(X))))) = and(neg(X2),or(and(neg(X2),neg(neg(X2))),neg(or(or(X2,neg(X2)),neg(X))))),
inference(congruence,[status(thm)],[c1521]) ).
cnf(c1523,plain,
neg(or(X,neg(X))) = and(neg(X),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1524,plain,
and(neg(X),neg(neg(X))) = neg(or(X,neg(X))),
inference(symmetry,[status(thm)],[c1523]) ).
cnf(c1525,plain,
or(and(neg(X2),neg(neg(X2))),neg(or(or(X2,neg(X2)),neg(X)))) = or(neg(or(X2,neg(X2))),neg(or(or(X2,neg(X2)),neg(X)))),
inference(congruence,[status(thm)],[c1524]) ).
cnf(c1526,plain,
and(neg(X2),or(and(neg(X2),neg(neg(X2))),neg(or(or(X2,neg(X2)),neg(X))))) = and(neg(X2),or(neg(or(X2,neg(X2))),neg(or(or(X2,neg(X2)),neg(X))))),
inference(congruence,[status(thm)],[c1525]) ).
cnf(c1527,plain,
f(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))) = or(neg(or(X2,neg(X2))),neg(or(or(X2,neg(X2)),neg(X)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1528,plain,
or(neg(or(X2,neg(X2))),neg(or(or(X2,neg(X2)),neg(X)))) = f(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))),
inference(symmetry,[status(thm)],[c1527]) ).
cnf(c1529,plain,
and(neg(X2),or(neg(or(X2,neg(X2))),neg(or(or(X2,neg(X2)),neg(X))))) = and(neg(X2),f(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X)))),
inference(congruence,[status(thm)],[c1528]) ).
cnf(c1530,plain,
neg(and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X)))) = f(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1531,plain,
f(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))) = neg(and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X)))),
inference(symmetry,[status(thm)],[c1530]) ).
cnf(c1532,plain,
and(neg(X2),f(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X)))) = and(neg(X2),neg(and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))))),
inference(congruence,[status(thm)],[c1531]) ).
cnf(c1533,plain,
neg(or(X2,and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))))) = and(neg(X2),neg(and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1534,plain,
and(neg(X2),neg(and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))))) = neg(or(X2,and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))))),
inference(symmetry,[status(thm)],[c1533]) ).
cnf(c1535,plain,
neg(neg(or(X,neg(X)))) = or(X,neg(X)),
inference(substitution,[status(thm)],[c79]) ).
cnf(c1536,plain,
or(X,neg(X)) = neg(neg(or(X,neg(X)))),
inference(symmetry,[status(thm)],[c1535]) ).
cnf(c1537,plain,
or(or(X2,neg(X2)),neg(X)) = or(neg(neg(or(X2,neg(X2)))),neg(X)),
inference(congruence,[status(thm)],[c1536]) ).
cnf(c1538,plain,
and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))) = and(or(X2,neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X))),
inference(congruence,[status(thm)],[c1537]) ).
cnf(c1539,plain,
or(X2,and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X)))) = or(X2,and(or(X2,neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X)))),
inference(congruence,[status(thm)],[c1538]) ).
cnf(c1540,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1541,plain,
or(X2,and(or(X2,neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X)))) = or(neg(neg(X2)),and(or(X2,neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X)))),
inference(congruence,[status(thm)],[c1540]) ).
cnf(c1542,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1543,plain,
or(X,neg(X)) = or(neg(neg(X)),neg(X)),
inference(congruence,[status(thm)],[c1542]) ).
cnf(c1544,plain,
and(or(X2,neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X))) = and(or(neg(neg(X2)),neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X))),
inference(congruence,[status(thm)],[c1543]) ).
cnf(c1545,plain,
or(neg(neg(X2)),and(or(X2,neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X)))) = or(neg(neg(X2)),and(or(neg(neg(X2)),neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X)))),
inference(congruence,[status(thm)],[c1544]) ).
cnf(c1546,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1547,plain,
or(X,neg(X)) = or(neg(neg(X)),neg(X)),
inference(congruence,[status(thm)],[c1546]) ).
cnf(c1548,plain,
neg(or(X,neg(X))) = neg(or(neg(neg(X)),neg(X))),
inference(congruence,[status(thm)],[c1547]) ).
cnf(c1549,plain,
neg(neg(or(X,neg(X)))) = neg(neg(or(neg(neg(X)),neg(X)))),
inference(congruence,[status(thm)],[c1548]) ).
cnf(c1550,plain,
or(neg(neg(or(X2,neg(X2)))),neg(X)) = or(neg(neg(or(neg(neg(X2)),neg(X2)))),neg(X)),
inference(congruence,[status(thm)],[c1549]) ).
cnf(c1551,plain,
and(or(neg(neg(X2)),neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X))) = and(or(neg(neg(X2)),neg(X2)),or(neg(neg(or(neg(neg(X2)),neg(X2)))),neg(X))),
inference(congruence,[status(thm)],[c1550]) ).
cnf(c1552,plain,
or(neg(neg(X2)),and(or(neg(neg(X2)),neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X)))) = or(neg(neg(X2)),and(or(neg(neg(X2)),neg(X2)),or(neg(neg(or(neg(neg(X2)),neg(X2)))),neg(X)))),
inference(congruence,[status(thm)],[c1551]) ).
cnf(c1553,plain,
and(or(neg(neg(X)),neg(X)),or(neg(neg(X)),neg(X))) = neg(neg(or(neg(neg(X)),neg(X)))),
inference(substitution,[status(thm)],[c122]) ).
cnf(c1554,plain,
neg(neg(or(neg(neg(X)),neg(X)))) = and(or(neg(neg(X)),neg(X)),or(neg(neg(X)),neg(X))),
inference(symmetry,[status(thm)],[c1553]) ).
cnf(c1555,plain,
or(neg(neg(or(neg(neg(X2)),neg(X2)))),neg(X)) = or(and(or(neg(neg(X2)),neg(X2)),or(neg(neg(X2)),neg(X2))),neg(X)),
inference(congruence,[status(thm)],[c1554]) ).
cnf(c1556,plain,
and(or(neg(neg(X2)),neg(X2)),or(neg(neg(or(neg(neg(X2)),neg(X2)))),neg(X))) = and(or(neg(neg(X2)),neg(X2)),or(and(or(neg(neg(X2)),neg(X2)),or(neg(neg(X2)),neg(X2))),neg(X))),
inference(congruence,[status(thm)],[c1555]) ).
cnf(c1557,plain,
or(neg(neg(X2)),and(or(neg(neg(X2)),neg(X2)),or(neg(neg(or(neg(neg(X2)),neg(X2)))),neg(X)))) = or(neg(neg(X2)),and(or(neg(neg(X2)),neg(X2)),or(and(or(neg(neg(X2)),neg(X2)),or(neg(neg(X2)),neg(X2))),neg(X)))),
inference(congruence,[status(thm)],[c1556]) ).
cnf(c1558,plain,
or(neg(neg(X2)),and(or(neg(neg(X2)),neg(X2)),or(and(or(neg(neg(X2)),neg(X2)),or(neg(neg(X2)),neg(X2))),neg(X)))) = or(neg(neg(X2)),neg(X2)),
inference(substitution,[status(thm)],[c495]) ).
cnf(c1559,plain,
or(neg(neg(X)),neg(X)) = or(X,neg(X)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c1560,plain,
or(neg(neg(X2)),and(or(neg(neg(X2)),neg(X2)),or(and(or(neg(neg(X2)),neg(X2)),or(neg(neg(X2)),neg(X2))),neg(X)))) = or(X2,neg(X2)),
inference(transitivity,[status(thm)],[c1558,c1559]) ).
cnf(c1561,plain,
or(neg(neg(X2)),and(or(neg(neg(X2)),neg(X2)),or(neg(neg(or(neg(neg(X2)),neg(X2)))),neg(X)))) = or(X2,neg(X2)),
inference(transitivity,[status(thm)],[c1557,c1560]) ).
cnf(c1562,plain,
or(neg(neg(X2)),and(or(neg(neg(X2)),neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X)))) = or(X2,neg(X2)),
inference(transitivity,[status(thm)],[c1552,c1561]) ).
cnf(c1563,plain,
or(neg(neg(X2)),and(or(X2,neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X)))) = or(X2,neg(X2)),
inference(transitivity,[status(thm)],[c1545,c1562]) ).
cnf(c1564,plain,
or(X2,and(or(X2,neg(X2)),or(neg(neg(or(X2,neg(X2)))),neg(X)))) = or(X2,neg(X2)),
inference(transitivity,[status(thm)],[c1541,c1563]) ).
cnf(c1565,plain,
or(X2,and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X)))) = or(X2,neg(X2)),
inference(transitivity,[status(thm)],[c1539,c1564]) ).
cnf(c1566,plain,
neg(or(X2,and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))))) = neg(or(X2,neg(X2))),
inference(congruence,[status(thm)],[c1565]) ).
cnf(c1567,plain,
neg(or(X,neg(X))) = and(neg(X),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1568,plain,
and(neg(X),neg(neg(X))) = and(neg(X),X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c1569,plain,
neg(or(X,neg(X))) = and(neg(X),X),
inference(transitivity,[status(thm)],[c1567,c1568]) ).
cnf(c1570,plain,
neg(or(X2,and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))))) = and(neg(X2),X2),
inference(transitivity,[status(thm)],[c1566,c1569]) ).
cnf(c1571,plain,
and(neg(X2),neg(and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))))) = and(neg(X2),X2),
inference(transitivity,[status(thm)],[c1534,c1570]) ).
cnf(c1572,plain,
and(neg(X2),f(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X)))) = and(neg(X2),X2),
inference(transitivity,[status(thm)],[c1532,c1571]) ).
cnf(c1573,plain,
and(neg(X2),or(neg(or(X2,neg(X2))),neg(or(or(X2,neg(X2)),neg(X))))) = and(neg(X2),X2),
inference(transitivity,[status(thm)],[c1529,c1572]) ).
cnf(c1574,plain,
and(neg(X2),or(and(neg(X2),neg(neg(X2))),neg(or(or(X2,neg(X2)),neg(X))))) = and(neg(X2),X2),
inference(transitivity,[status(thm)],[c1526,c1573]) ).
cnf(c1575,plain,
and(neg(X2),or(and(neg(X2),X2),neg(or(or(X2,neg(X2)),neg(X))))) = and(neg(X2),X2),
inference(transitivity,[status(thm)],[c1522,c1574]) ).
cnf(c1576,plain,
and(neg(X2),or(and(neg(X2),X2),and(neg(or(X2,neg(X2))),neg(neg(X))))) = and(neg(X2),X2),
inference(transitivity,[status(thm)],[c1518,c1575]) ).
cnf(c1577,plain,
and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),neg(neg(X2))),neg(neg(X))))) = and(neg(X2),X2),
inference(transitivity,[status(thm)],[c1514,c1576]) ).
cnf(c1578,plain,
and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),X2),neg(neg(X))))) = and(neg(X2),X2),
inference(transitivity,[status(thm)],[c1509,c1577]) ).
cnf(c1579,plain,
and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),X2),X))) = and(neg(X2),X2),
inference(transitivity,[status(thm)],[c1504,c1578]) ).
cnf(c1580,plain,
and(neg(X2),X2) = and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),X2),X))),
inference(symmetry,[status(thm)],[c1579]) ).
cnf(c1581,plain,
and(and(neg(X2),X2),or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X))))) = and(and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),X2),X))),or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X))))),
inference(congruence,[status(thm)],[c1580]) ).
cnf(c1582,plain,
or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X)))))) = or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),X2),X))),or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X)))))),
inference(congruence,[status(thm)],[c1581]) ).
cnf(c1583,plain,
and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X))))))) = and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),X2),X))),or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X))))))),
inference(congruence,[status(thm)],[c1582]) ).
cnf(c1584,plain,
f(X,X2) = or(neg(X),neg(X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1585,plain,
or(neg(X),neg(X2)) = f(X,X2),
inference(symmetry,[status(thm)],[c1584]) ).
cnf(c1586,plain,
and(and(X,X2),or(neg(X),neg(X2))) = and(and(X,X2),f(X,X2)),
inference(congruence,[status(thm)],[c1585]) ).
cnf(c1587,plain,
or(and(X3,X2),and(and(X,X3),or(neg(X),neg(X3)))) = or(and(X3,X2),and(and(X,X3),f(X,X3))),
inference(congruence,[status(thm)],[c1586]) ).
cnf(c1588,plain,
and(X3,or(and(X3,X2),and(and(X,X3),or(neg(X),neg(X3))))) = and(X3,or(and(X3,X2),and(and(X,X3),f(X,X3)))),
inference(congruence,[status(thm)],[c1587]) ).
cnf(c1589,plain,
neg(and(X,X2)) = f(X,X2),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1590,plain,
f(X,X2) = neg(and(X,X2)),
inference(symmetry,[status(thm)],[c1589]) ).
cnf(c1591,plain,
and(and(X,X2),f(X,X2)) = and(and(X,X2),neg(and(X,X2))),
inference(congruence,[status(thm)],[c1590]) ).
cnf(c1592,plain,
or(and(X3,X2),and(and(X,X3),f(X,X3))) = or(and(X3,X2),and(and(X,X3),neg(and(X,X3)))),
inference(congruence,[status(thm)],[c1591]) ).
cnf(c1593,plain,
and(X3,or(and(X3,X2),and(and(X,X3),f(X,X3)))) = and(X3,or(and(X3,X2),and(and(X,X3),neg(and(X,X3))))),
inference(congruence,[status(thm)],[c1592]) ).
cnf(c1594,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1595,plain,
and(X,X2) = and(X,neg(neg(X2))),
inference(congruence,[status(thm)],[c1594]) ).
cnf(c1596,plain,
and(and(X,X2),neg(and(X,X2))) = and(and(X,neg(neg(X2))),neg(and(X,X2))),
inference(congruence,[status(thm)],[c1595]) ).
cnf(c1597,plain,
or(and(X3,X2),and(and(X,X3),neg(and(X,X3)))) = or(and(X3,X2),and(and(X,neg(neg(X3))),neg(and(X,X3)))),
inference(congruence,[status(thm)],[c1596]) ).
cnf(c1598,plain,
and(X3,or(and(X3,X2),and(and(X,X3),neg(and(X,X3))))) = and(X3,or(and(X3,X2),and(and(X,neg(neg(X3))),neg(and(X,X3))))),
inference(congruence,[status(thm)],[c1597]) ).
cnf(c1599,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1600,plain,
and(X,neg(neg(X2))) = and(neg(neg(X)),neg(neg(X2))),
inference(congruence,[status(thm)],[c1599]) ).
cnf(c1601,plain,
and(and(X,neg(neg(X2))),neg(and(X,X2))) = and(and(neg(neg(X)),neg(neg(X2))),neg(and(X,X2))),
inference(congruence,[status(thm)],[c1600]) ).
cnf(c1602,plain,
or(and(X3,X2),and(and(X,neg(neg(X3))),neg(and(X,X3)))) = or(and(X3,X2),and(and(neg(neg(X)),neg(neg(X3))),neg(and(X,X3)))),
inference(congruence,[status(thm)],[c1601]) ).
cnf(c1603,plain,
and(X3,or(and(X3,X2),and(and(X,neg(neg(X3))),neg(and(X,X3))))) = and(X3,or(and(X3,X2),and(and(neg(neg(X)),neg(neg(X3))),neg(and(X,X3))))),
inference(congruence,[status(thm)],[c1602]) ).
cnf(c1604,plain,
neg(or(neg(X),neg(X2))) = and(neg(neg(X)),neg(neg(X2))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1605,plain,
and(neg(neg(X)),neg(neg(X2))) = neg(or(neg(X),neg(X2))),
inference(symmetry,[status(thm)],[c1604]) ).
cnf(c1606,plain,
and(and(neg(neg(X)),neg(neg(X2))),neg(and(X,X2))) = and(neg(or(neg(X),neg(X2))),neg(and(X,X2))),
inference(congruence,[status(thm)],[c1605]) ).
cnf(c1607,plain,
or(and(X3,X2),and(and(neg(neg(X)),neg(neg(X3))),neg(and(X,X3)))) = or(and(X3,X2),and(neg(or(neg(X),neg(X3))),neg(and(X,X3)))),
inference(congruence,[status(thm)],[c1606]) ).
cnf(c1608,plain,
and(X3,or(and(X3,X2),and(and(neg(neg(X)),neg(neg(X3))),neg(and(X,X3))))) = and(X3,or(and(X3,X2),and(neg(or(neg(X),neg(X3))),neg(and(X,X3))))),
inference(congruence,[status(thm)],[c1607]) ).
cnf(c1609,plain,
neg(or(or(neg(X),neg(X2)),and(X,X2))) = and(neg(or(neg(X),neg(X2))),neg(and(X,X2))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1610,plain,
and(neg(or(neg(X),neg(X2))),neg(and(X,X2))) = neg(or(or(neg(X),neg(X2)),and(X,X2))),
inference(symmetry,[status(thm)],[c1609]) ).
cnf(c1611,plain,
or(and(X3,X2),and(neg(or(neg(X),neg(X3))),neg(and(X,X3)))) = or(and(X3,X2),neg(or(or(neg(X),neg(X3)),and(X,X3)))),
inference(congruence,[status(thm)],[c1610]) ).
cnf(c1612,plain,
and(X3,or(and(X3,X2),and(neg(or(neg(X),neg(X3))),neg(and(X,X3))))) = and(X3,or(and(X3,X2),neg(or(or(neg(X),neg(X3)),and(X,X3))))),
inference(congruence,[status(thm)],[c1611]) ).
cnf(c1613,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1614,plain,
and(X2,X) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c1613]) ).
cnf(c1615,plain,
or(and(X3,X2),neg(or(or(neg(X),neg(X3)),and(X,X3)))) = or(and(X3,neg(neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3)))),
inference(congruence,[status(thm)],[c1614]) ).
cnf(c1616,plain,
and(X3,or(and(X3,X2),neg(or(or(neg(X),neg(X3)),and(X,X3))))) = and(X3,or(and(X3,neg(neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3))))),
inference(congruence,[status(thm)],[c1615]) ).
cnf(c1617,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1618,plain,
and(X2,neg(neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(congruence,[status(thm)],[c1617]) ).
cnf(c1619,plain,
or(and(X3,neg(neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3)))) = or(and(neg(neg(X3)),neg(neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3)))),
inference(congruence,[status(thm)],[c1618]) ).
cnf(c1620,plain,
and(X3,or(and(X3,neg(neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3))))) = and(X3,or(and(neg(neg(X3)),neg(neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3))))),
inference(congruence,[status(thm)],[c1619]) ).
cnf(c1621,plain,
neg(or(neg(X2),neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1622,plain,
and(neg(neg(X2)),neg(neg(X))) = neg(or(neg(X2),neg(X))),
inference(symmetry,[status(thm)],[c1621]) ).
cnf(c1623,plain,
or(and(neg(neg(X3)),neg(neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3)))) = or(neg(or(neg(X3),neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3)))),
inference(congruence,[status(thm)],[c1622]) ).
cnf(c1624,plain,
and(X3,or(and(neg(neg(X3)),neg(neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3))))) = and(X3,or(neg(or(neg(X3),neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3))))),
inference(congruence,[status(thm)],[c1623]) ).
cnf(c1625,plain,
f(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))) = or(neg(or(neg(X3),neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1626,plain,
or(neg(or(neg(X3),neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3)))) = f(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))),
inference(symmetry,[status(thm)],[c1625]) ).
cnf(c1627,plain,
and(X3,or(neg(or(neg(X3),neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3))))) = and(X3,f(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3)))),
inference(congruence,[status(thm)],[c1626]) ).
cnf(c1628,plain,
neg(and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3)))) = f(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1629,plain,
f(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))) = neg(and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3)))),
inference(symmetry,[status(thm)],[c1628]) ).
cnf(c1630,plain,
and(X3,f(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3)))) = and(X3,neg(and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))))),
inference(congruence,[status(thm)],[c1629]) ).
cnf(c1631,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1632,plain,
and(X3,neg(and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))))) = and(neg(neg(X3)),neg(and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))))),
inference(congruence,[status(thm)],[c1631]) ).
cnf(c1633,plain,
neg(or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))))) = and(neg(neg(X3)),neg(and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1634,plain,
and(neg(neg(X3)),neg(and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))))) = neg(or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))))),
inference(symmetry,[status(thm)],[c1633]) ).
cnf(c1635,plain,
neg(or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))))) = neg(or(neg(X3),neg(X2))),
inference(congruence,[status(thm)],[c327]) ).
cnf(c1636,plain,
neg(or(neg(X2),neg(X))) = and(neg(neg(X2)),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1637,plain,
and(neg(neg(X2)),neg(neg(X))) = and(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c1638,plain,
and(X2,neg(neg(X))) = and(X2,X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c1639,plain,
and(neg(neg(X2)),neg(neg(X))) = and(X2,X),
inference(transitivity,[status(thm)],[c1637,c1638]) ).
cnf(c1640,plain,
neg(or(neg(X2),neg(X))) = and(X2,X),
inference(transitivity,[status(thm)],[c1636,c1639]) ).
cnf(c1641,plain,
neg(or(neg(X3),and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1635,c1640]) ).
cnf(c1642,plain,
and(neg(neg(X3)),neg(and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1634,c1641]) ).
cnf(c1643,plain,
and(X3,neg(and(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1632,c1642]) ).
cnf(c1644,plain,
and(X3,f(or(neg(X3),neg(X2)),or(or(neg(X),neg(X3)),and(X,X3)))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1630,c1643]) ).
cnf(c1645,plain,
and(X3,or(neg(or(neg(X3),neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1627,c1644]) ).
cnf(c1646,plain,
and(X3,or(and(neg(neg(X3)),neg(neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1624,c1645]) ).
cnf(c1647,plain,
and(X3,or(and(X3,neg(neg(X2))),neg(or(or(neg(X),neg(X3)),and(X,X3))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1620,c1646]) ).
cnf(c1648,plain,
and(X3,or(and(X3,X2),neg(or(or(neg(X),neg(X3)),and(X,X3))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1616,c1647]) ).
cnf(c1649,plain,
and(X3,or(and(X3,X2),and(neg(or(neg(X),neg(X3))),neg(and(X,X3))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1612,c1648]) ).
cnf(c1650,plain,
and(X3,or(and(X3,X2),and(and(neg(neg(X)),neg(neg(X3))),neg(and(X,X3))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1608,c1649]) ).
cnf(c1651,plain,
and(X3,or(and(X3,X2),and(and(X,neg(neg(X3))),neg(and(X,X3))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1603,c1650]) ).
cnf(c1652,plain,
and(X3,or(and(X3,X2),and(and(X,X3),neg(and(X,X3))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1598,c1651]) ).
cnf(c1653,plain,
and(X3,or(and(X3,X2),and(and(X,X3),f(X,X3)))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1593,c1652]) ).
cnf(c1654,plain,
and(X3,or(and(X3,X2),and(and(X,X3),or(neg(X),neg(X3))))) = and(X3,X2),
inference(transitivity,[status(thm)],[c1588,c1653]) ).
cnf(c1655,plain,
and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),X2),X))),or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X))))))) = and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),
inference(substitution,[status(thm)],[c1654]) ).
cnf(c1656,plain,
or(and(neg(X2),X2),and(and(neg(X2),X2),X)) = and(neg(X2),X2),
inference(substitution,[status(thm)],[c1485]) ).
cnf(c1657,plain,
and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3) = and(and(neg(X2),X2),X3),
inference(congruence,[status(thm)],[c1656]) ).
cnf(c1658,plain,
and(neg(X),X) = and(X,neg(X)),
inference(substitution,[status(thm)],[c930]) ).
cnf(c1659,plain,
and(and(neg(X),X),X2) = and(and(X,neg(X)),X2),
inference(congruence,[status(thm)],[c1658]) ).
cnf(c1660,plain,
and(X2,and(X,neg(X))) = and(and(X,neg(X)),X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c1661,plain,
and(and(X,neg(X)),X2) = and(X2,and(X,neg(X))),
inference(symmetry,[status(thm)],[c1660]) ).
cnf(c1662,plain,
and(and(neg(X),X),X2) = and(X2,and(X,neg(X))),
inference(transitivity,[status(thm)],[c1659,c1661]) ).
cnf(c1663,plain,
and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3) = and(X3,and(X2,neg(X2))),
inference(transitivity,[status(thm)],[c1657,c1662]) ).
cnf(c1664,plain,
and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),or(and(neg(X2),X2),and(and(neg(X2),X2),X))),or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X))))))) = and(X3,and(X2,neg(X2))),
inference(transitivity,[status(thm)],[c1655,c1663]) ).
cnf(c1665,plain,
and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(or(and(neg(X2),X2),and(and(neg(X2),X2),X))))))) = and(X3,and(X2,neg(X2))),
inference(transitivity,[status(thm)],[c1583,c1664]) ).
cnf(c1666,plain,
and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),or(and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(and(neg(X2),X2)))))) = and(X3,and(X2,neg(X2))),
inference(transitivity,[status(thm)],[c1500,c1665]) ).
cnf(c1667,plain,
and(or(and(neg(X2),X2),and(and(neg(X2),X2),X)),or(and(and(neg(X2),X2),X3),and(and(neg(X2),X2),or(neg(neg(X2)),neg(and(neg(X2),X2)))))) = and(X3,and(X2,neg(X2))),
inference(transitivity,[status(thm)],[c1493,c1666]) ).
cnf(c1668,plain,
and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(neg(neg(X)),neg(and(neg(X),X)))))) = and(X2,and(X,neg(X))),
inference(transitivity,[status(thm)],[c1488,c1667]) ).
cnf(c1669,plain,
and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(and(neg(X),X)))))) = and(X2,and(X,neg(X))),
inference(transitivity,[status(thm)],[c1445,c1668]) ).
cnf(c1670,plain,
and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,f(neg(X),X))))) = and(X2,and(X,neg(X))),
inference(transitivity,[status(thm)],[c1440,c1669]) ).
cnf(c1671,plain,
and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,or(X,neg(X)))))) = and(X2,and(X,neg(X))),
inference(transitivity,[status(thm)],[c1434,c1670]) ).
cnf(c1672,plain,
and(and(neg(X),X),or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(X))))) = and(X2,and(X,neg(X))),
inference(transitivity,[status(thm)],[c1428,c1671]) ).
cnf(c1673,plain,
or(and(and(neg(X),X),X2),and(and(neg(X),X),or(X,neg(X)))) = and(X2,and(X,neg(X))),
inference(transitivity,[status(thm)],[c1404,c1672]) ).
cnf(c1674,plain,
or(and(and(neg(X),X),X2),and(and(X,neg(X)),or(X,neg(X)))) = and(X2,and(X,neg(X))),
inference(transitivity,[status(thm)],[c1296,c1673]) ).
cnf(c1675,plain,
or(and(and(X,neg(X)),X2),and(and(X,neg(X)),or(X,neg(X)))) = and(X2,and(X,neg(X))),
inference(transitivity,[status(thm)],[c1292,c1674]) ).
cnf(c1676,plain,
or(and(and(X,neg(X)),X2),and(or(X,neg(X)),and(X,neg(X)))) = and(X2,and(X,neg(X))),
inference(transitivity,[status(thm)],[c1288,c1675]) ).
cnf(c1677,plain,
or(and(X2,and(X,neg(X))),and(or(X,neg(X)),and(X,neg(X)))) = and(X2,and(X,neg(X))),
inference(transitivity,[status(thm)],[c1286,c1676]) ).
cnf(c1678,plain,
and(X2,and(X,neg(X))) = or(and(X2,and(X,neg(X))),and(or(X,neg(X)),and(X,neg(X)))),
inference(symmetry,[status(thm)],[c1677]) ).
cnf(c1679,plain,
and(or(X2,neg(X)),and(X,neg(X))) = and(and(X,neg(X)),or(X2,neg(X))),
inference(substitution,[status(thm)],[c934]) ).
cnf(c1680,plain,
and(X,neg(X2)) = and(neg(X2),X),
inference(symmetry,[status(thm)],[c930]) ).
cnf(c1681,plain,
or(or(X2,neg(X)),and(X,neg(X2))) = or(or(X2,neg(X)),and(neg(X2),X)),
inference(congruence,[status(thm)],[c1680]) ).
cnf(c1682,plain,
and(neg(X2),or(or(X2,neg(X)),and(X,neg(X2)))) = and(neg(X2),or(or(X2,neg(X)),and(neg(X2),X))),
inference(congruence,[status(thm)],[c1681]) ).
cnf(c1683,plain,
or(or(X2,neg(X)),and(neg(X2),X)) = or(and(neg(X2),X),or(X2,neg(X))),
inference(substitution,[status(thm)],[c913]) ).
cnf(c1684,plain,
and(neg(X2),or(or(X2,neg(X)),and(neg(X2),X))) = and(neg(X2),or(and(neg(X2),X),or(X2,neg(X)))),
inference(congruence,[status(thm)],[c1683]) ).
cnf(c1685,plain,
and(neg(X2),or(and(neg(X2),X),or(X2,neg(X)))) = and(or(and(neg(X2),X),or(X2,neg(X))),neg(X2)),
inference(substitution,[status(thm)],[c930]) ).
cnf(c1686,plain,
or(X2,neg(X)) = f(neg(X2),X),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c1687,plain,
or(and(neg(X2),X),or(X2,neg(X))) = or(and(neg(X2),X),f(neg(X2),X)),
inference(congruence,[status(thm)],[c1686]) ).
cnf(c1688,plain,
and(neg(X2),or(and(neg(X2),X),or(X2,neg(X)))) = and(neg(X2),or(and(neg(X2),X),f(neg(X2),X))),
inference(congruence,[status(thm)],[c1687]) ).
cnf(c1689,plain,
or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),or(X2,neg(X))))) = or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),f(neg(X2),X)))),
inference(congruence,[status(thm)],[c1688]) ).
cnf(c1690,plain,
neg(and(neg(X2),X)) = f(neg(X2),X),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1691,plain,
f(neg(X2),X) = neg(and(neg(X2),X)),
inference(symmetry,[status(thm)],[c1690]) ).
cnf(c1692,plain,
or(and(neg(X2),X),f(neg(X2),X)) = or(and(neg(X2),X),neg(and(neg(X2),X))),
inference(congruence,[status(thm)],[c1691]) ).
cnf(c1693,plain,
and(neg(X2),or(and(neg(X2),X),f(neg(X2),X))) = and(neg(X2),or(and(neg(X2),X),neg(and(neg(X2),X)))),
inference(congruence,[status(thm)],[c1692]) ).
cnf(c1694,plain,
or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),f(neg(X2),X)))) = or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),neg(and(neg(X2),X))))),
inference(congruence,[status(thm)],[c1693]) ).
cnf(c1695,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1696,plain,
and(neg(X2),X) = and(neg(X2),neg(neg(X))),
inference(congruence,[status(thm)],[c1695]) ).
cnf(c1697,plain,
or(and(neg(X2),X),neg(and(neg(X2),X))) = or(and(neg(X2),neg(neg(X))),neg(and(neg(X2),X))),
inference(congruence,[status(thm)],[c1696]) ).
cnf(c1698,plain,
and(neg(X2),or(and(neg(X2),X),neg(and(neg(X2),X)))) = and(neg(X2),or(and(neg(X2),neg(neg(X))),neg(and(neg(X2),X)))),
inference(congruence,[status(thm)],[c1697]) ).
cnf(c1699,plain,
or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),neg(and(neg(X2),X))))) = or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),neg(neg(X))),neg(and(neg(X2),X))))),
inference(congruence,[status(thm)],[c1698]) ).
cnf(c1700,plain,
neg(or(X2,neg(X))) = and(neg(X2),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1701,plain,
and(neg(X2),neg(neg(X))) = neg(or(X2,neg(X))),
inference(symmetry,[status(thm)],[c1700]) ).
cnf(c1702,plain,
or(and(neg(X2),neg(neg(X))),neg(and(neg(X2),X))) = or(neg(or(X2,neg(X))),neg(and(neg(X2),X))),
inference(congruence,[status(thm)],[c1701]) ).
cnf(c1703,plain,
and(neg(X2),or(and(neg(X2),neg(neg(X))),neg(and(neg(X2),X)))) = and(neg(X2),or(neg(or(X2,neg(X))),neg(and(neg(X2),X)))),
inference(congruence,[status(thm)],[c1702]) ).
cnf(c1704,plain,
or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),neg(neg(X))),neg(and(neg(X2),X))))) = or(and(neg(X2),X),and(neg(X2),or(neg(or(X2,neg(X))),neg(and(neg(X2),X))))),
inference(congruence,[status(thm)],[c1703]) ).
cnf(c1705,plain,
f(or(X2,neg(X)),and(neg(X2),X)) = or(neg(or(X2,neg(X))),neg(and(neg(X2),X))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1706,plain,
or(neg(or(X2,neg(X))),neg(and(neg(X2),X))) = f(or(X2,neg(X)),and(neg(X2),X)),
inference(symmetry,[status(thm)],[c1705]) ).
cnf(c1707,plain,
and(neg(X2),or(neg(or(X2,neg(X))),neg(and(neg(X2),X)))) = and(neg(X2),f(or(X2,neg(X)),and(neg(X2),X))),
inference(congruence,[status(thm)],[c1706]) ).
cnf(c1708,plain,
or(and(neg(X2),X),and(neg(X2),or(neg(or(X2,neg(X))),neg(and(neg(X2),X))))) = or(and(neg(X2),X),and(neg(X2),f(or(X2,neg(X)),and(neg(X2),X)))),
inference(congruence,[status(thm)],[c1707]) ).
cnf(c1709,plain,
neg(and(or(X2,neg(X)),and(neg(X2),X))) = f(or(X2,neg(X)),and(neg(X2),X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1710,plain,
f(or(X2,neg(X)),and(neg(X2),X)) = neg(and(or(X2,neg(X)),and(neg(X2),X))),
inference(symmetry,[status(thm)],[c1709]) ).
cnf(c1711,plain,
and(neg(X2),f(or(X2,neg(X)),and(neg(X2),X))) = and(neg(X2),neg(and(or(X2,neg(X)),and(neg(X2),X)))),
inference(congruence,[status(thm)],[c1710]) ).
cnf(c1712,plain,
or(and(neg(X2),X),and(neg(X2),f(or(X2,neg(X)),and(neg(X2),X)))) = or(and(neg(X2),X),and(neg(X2),neg(and(or(X2,neg(X)),and(neg(X2),X))))),
inference(congruence,[status(thm)],[c1711]) ).
cnf(c1713,plain,
neg(or(X2,and(or(X2,neg(X)),and(neg(X2),X)))) = and(neg(X2),neg(and(or(X2,neg(X)),and(neg(X2),X)))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1714,plain,
and(neg(X2),neg(and(or(X2,neg(X)),and(neg(X2),X)))) = neg(or(X2,and(or(X2,neg(X)),and(neg(X2),X)))),
inference(symmetry,[status(thm)],[c1713]) ).
cnf(c1715,plain,
or(and(neg(X2),X),and(neg(X2),neg(and(or(X2,neg(X)),and(neg(X2),X))))) = or(and(neg(X2),X),neg(or(X2,and(or(X2,neg(X)),and(neg(X2),X))))),
inference(congruence,[status(thm)],[c1714]) ).
cnf(c1716,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1717,plain,
and(neg(X2),X) = and(neg(X2),neg(neg(X))),
inference(congruence,[status(thm)],[c1716]) ).
cnf(c1718,plain,
or(and(neg(X2),X),neg(or(X2,and(or(X2,neg(X)),and(neg(X2),X))))) = or(and(neg(X2),neg(neg(X))),neg(or(X2,and(or(X2,neg(X)),and(neg(X2),X))))),
inference(congruence,[status(thm)],[c1717]) ).
cnf(c1719,plain,
neg(or(X2,neg(X))) = and(neg(X2),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1720,plain,
and(neg(X2),neg(neg(X))) = neg(or(X2,neg(X))),
inference(symmetry,[status(thm)],[c1719]) ).
cnf(c1721,plain,
or(and(neg(X2),neg(neg(X))),neg(or(X2,and(or(X2,neg(X)),and(neg(X2),X))))) = or(neg(or(X2,neg(X))),neg(or(X2,and(or(X2,neg(X)),and(neg(X2),X))))),
inference(congruence,[status(thm)],[c1720]) ).
cnf(c1722,plain,
f(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X)))) = or(neg(or(X2,neg(X))),neg(or(X2,and(or(X2,neg(X)),and(neg(X2),X))))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1723,plain,
or(neg(or(X2,neg(X))),neg(or(X2,and(or(X2,neg(X)),and(neg(X2),X))))) = f(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X)))),
inference(symmetry,[status(thm)],[c1722]) ).
cnf(c1724,plain,
neg(and(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X))))) = f(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X)))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1725,plain,
f(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X)))) = neg(and(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X))))),
inference(symmetry,[status(thm)],[c1724]) ).
cnf(c1726,plain,
neg(and(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X))))) = neg(X2),
inference(congruence,[status(thm)],[c974]) ).
cnf(c1727,plain,
f(or(X2,neg(X)),or(X2,and(or(X2,neg(X)),and(neg(X2),X)))) = neg(X2),
inference(transitivity,[status(thm)],[c1725,c1726]) ).
cnf(c1728,plain,
or(neg(or(X2,neg(X))),neg(or(X2,and(or(X2,neg(X)),and(neg(X2),X))))) = neg(X2),
inference(transitivity,[status(thm)],[c1723,c1727]) ).
cnf(c1729,plain,
or(and(neg(X2),neg(neg(X))),neg(or(X2,and(or(X2,neg(X)),and(neg(X2),X))))) = neg(X2),
inference(transitivity,[status(thm)],[c1721,c1728]) ).
cnf(c1730,plain,
or(and(neg(X2),X),neg(or(X2,and(or(X2,neg(X)),and(neg(X2),X))))) = neg(X2),
inference(transitivity,[status(thm)],[c1718,c1729]) ).
cnf(c1731,plain,
or(and(neg(X2),X),and(neg(X2),neg(and(or(X2,neg(X)),and(neg(X2),X))))) = neg(X2),
inference(transitivity,[status(thm)],[c1715,c1730]) ).
cnf(c1732,plain,
or(and(neg(X2),X),and(neg(X2),f(or(X2,neg(X)),and(neg(X2),X)))) = neg(X2),
inference(transitivity,[status(thm)],[c1712,c1731]) ).
cnf(c1733,plain,
or(and(neg(X2),X),and(neg(X2),or(neg(or(X2,neg(X))),neg(and(neg(X2),X))))) = neg(X2),
inference(transitivity,[status(thm)],[c1708,c1732]) ).
cnf(c1734,plain,
or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),neg(neg(X))),neg(and(neg(X2),X))))) = neg(X2),
inference(transitivity,[status(thm)],[c1704,c1733]) ).
cnf(c1735,plain,
or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),neg(and(neg(X2),X))))) = neg(X2),
inference(transitivity,[status(thm)],[c1699,c1734]) ).
cnf(c1736,plain,
or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),f(neg(X2),X)))) = neg(X2),
inference(transitivity,[status(thm)],[c1694,c1735]) ).
cnf(c1737,plain,
or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),or(X2,neg(X))))) = neg(X2),
inference(transitivity,[status(thm)],[c1689,c1736]) ).
cnf(c1738,plain,
neg(X2) = or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),or(X2,neg(X))))),
inference(symmetry,[status(thm)],[c1737]) ).
cnf(c1739,plain,
and(or(and(neg(X2),X),or(X2,neg(X))),neg(X2)) = and(or(and(neg(X2),X),or(X2,neg(X))),or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),or(X2,neg(X)))))),
inference(congruence,[status(thm)],[c1738]) ).
cnf(c1740,plain,
and(or(and(neg(X2),X),or(X2,neg(X))),or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),or(X2,neg(X)))))) = or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),or(X2,neg(X))))),
inference(substitution,[status(thm)],[c1391]) ).
cnf(c1741,plain,
and(or(and(neg(X2),X),or(X2,neg(X))),or(and(neg(X2),X),and(neg(X2),or(and(neg(X2),X),or(X2,neg(X)))))) = neg(X2),
inference(transitivity,[status(thm)],[c1740,c1737]) ).
cnf(c1742,plain,
and(or(and(neg(X2),X),or(X2,neg(X))),neg(X2)) = neg(X2),
inference(transitivity,[status(thm)],[c1739,c1741]) ).
cnf(c1743,plain,
and(neg(X2),or(and(neg(X2),X),or(X2,neg(X)))) = neg(X2),
inference(transitivity,[status(thm)],[c1685,c1742]) ).
cnf(c1744,plain,
and(neg(X2),or(or(X2,neg(X)),and(neg(X2),X))) = neg(X2),
inference(transitivity,[status(thm)],[c1684,c1743]) ).
cnf(c1745,plain,
and(neg(X2),or(or(X2,neg(X)),and(X,neg(X2)))) = neg(X2),
inference(transitivity,[status(thm)],[c1682,c1744]) ).
cnf(c1746,plain,
and(neg(X),or(or(X,neg(X)),and(X,neg(X)))) = neg(X),
inference(substitution,[status(thm)],[c1745]) ).
cnf(c1747,plain,
neg(X) = and(neg(X),or(or(X,neg(X)),and(X,neg(X)))),
inference(symmetry,[status(thm)],[c1746]) ).
cnf(c1748,plain,
or(X2,neg(X)) = or(X2,and(neg(X),or(or(X,neg(X)),and(X,neg(X))))),
inference(congruence,[status(thm)],[c1747]) ).
cnf(c1749,plain,
and(and(X,neg(X)),or(X2,neg(X))) = and(and(X,neg(X)),or(X2,and(neg(X),or(or(X,neg(X)),and(X,neg(X)))))),
inference(congruence,[status(thm)],[c1748]) ).
cnf(c1750,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1751,plain,
or(X,and(X2,neg(X2))) = or(neg(neg(X)),and(X2,neg(X2))),
inference(congruence,[status(thm)],[c1750]) ).
cnf(c1752,plain,
and(neg(X2),or(X,and(X2,neg(X2)))) = and(neg(X2),or(neg(neg(X)),and(X2,neg(X2)))),
inference(congruence,[status(thm)],[c1751]) ).
cnf(c1753,plain,
or(X2,and(neg(X3),or(X,and(X3,neg(X3))))) = or(X2,and(neg(X3),or(neg(neg(X)),and(X3,neg(X3))))),
inference(congruence,[status(thm)],[c1752]) ).
cnf(c1754,plain,
and(and(X3,neg(X3)),or(X2,and(neg(X3),or(X,and(X3,neg(X3)))))) = and(and(X3,neg(X3)),or(X2,and(neg(X3),or(neg(neg(X)),and(X3,neg(X3)))))),
inference(congruence,[status(thm)],[c1753]) ).
cnf(c1755,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1756,plain,
or(X2,and(neg(X3),or(neg(X),and(X3,neg(X3))))) = or(neg(neg(X2)),and(neg(X3),or(neg(X),and(X3,neg(X3))))),
inference(congruence,[status(thm)],[c1755]) ).
cnf(c1757,plain,
and(and(X3,neg(X3)),or(X2,and(neg(X3),or(neg(X),and(X3,neg(X3)))))) = and(and(X3,neg(X3)),or(neg(neg(X2)),and(neg(X3),or(neg(X),and(X3,neg(X3)))))),
inference(congruence,[status(thm)],[c1756]) ).
cnf(c1758,plain,
and(neg(X),X) = and(X,neg(X)),
inference(substitution,[status(thm)],[c930]) ).
cnf(c1759,plain,
and(X,neg(X)) = and(neg(X),X),
inference(symmetry,[status(thm)],[c1758]) ).
cnf(c1760,plain,
and(and(X3,neg(X3)),or(neg(X2),and(neg(X3),or(neg(X),and(X3,neg(X3)))))) = and(and(neg(X3),X3),or(neg(X2),and(neg(X3),or(neg(X),and(X3,neg(X3)))))),
inference(congruence,[status(thm)],[c1759]) ).
cnf(c1761,plain,
and(neg(X),X) = and(X,neg(X)),
inference(substitution,[status(thm)],[c930]) ).
cnf(c1762,plain,
and(X,neg(X)) = and(neg(X),X),
inference(symmetry,[status(thm)],[c1761]) ).
cnf(c1763,plain,
or(neg(X),and(X2,neg(X2))) = or(neg(X),and(neg(X2),X2)),
inference(congruence,[status(thm)],[c1762]) ).
cnf(c1764,plain,
and(neg(X2),or(neg(X),and(X2,neg(X2)))) = and(neg(X2),or(neg(X),and(neg(X2),X2))),
inference(congruence,[status(thm)],[c1763]) ).
cnf(c1765,plain,
or(neg(X2),and(neg(X3),or(neg(X),and(X3,neg(X3))))) = or(neg(X2),and(neg(X3),or(neg(X),and(neg(X3),X3)))),
inference(congruence,[status(thm)],[c1764]) ).
cnf(c1766,plain,
and(and(neg(X3),X3),or(neg(X2),and(neg(X3),or(neg(X),and(X3,neg(X3)))))) = and(and(neg(X3),X3),or(neg(X2),and(neg(X3),or(neg(X),and(neg(X3),X3))))),
inference(congruence,[status(thm)],[c1765]) ).
cnf(c1767,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1768,plain,
and(neg(X),X) = and(neg(X),neg(neg(X))),
inference(congruence,[status(thm)],[c1767]) ).
cnf(c1769,plain,
or(neg(X),and(neg(X2),X2)) = or(neg(X),and(neg(X2),neg(neg(X2)))),
inference(congruence,[status(thm)],[c1768]) ).
cnf(c1770,plain,
and(neg(X2),or(neg(X),and(neg(X2),X2))) = and(neg(X2),or(neg(X),and(neg(X2),neg(neg(X2))))),
inference(congruence,[status(thm)],[c1769]) ).
cnf(c1771,plain,
or(neg(X2),and(neg(X3),or(neg(X),and(neg(X3),X3)))) = or(neg(X2),and(neg(X3),or(neg(X),and(neg(X3),neg(neg(X3)))))),
inference(congruence,[status(thm)],[c1770]) ).
cnf(c1772,plain,
and(and(neg(X3),X3),or(neg(X2),and(neg(X3),or(neg(X),and(neg(X3),X3))))) = and(and(neg(X3),X3),or(neg(X2),and(neg(X3),or(neg(X),and(neg(X3),neg(neg(X3))))))),
inference(congruence,[status(thm)],[c1771]) ).
cnf(c1773,plain,
neg(or(X,neg(X))) = and(neg(X),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1774,plain,
and(neg(X),neg(neg(X))) = neg(or(X,neg(X))),
inference(symmetry,[status(thm)],[c1773]) ).
cnf(c1775,plain,
or(neg(X),and(neg(X2),neg(neg(X2)))) = or(neg(X),neg(or(X2,neg(X2)))),
inference(congruence,[status(thm)],[c1774]) ).
cnf(c1776,plain,
and(neg(X2),or(neg(X),and(neg(X2),neg(neg(X2))))) = and(neg(X2),or(neg(X),neg(or(X2,neg(X2))))),
inference(congruence,[status(thm)],[c1775]) ).
cnf(c1777,plain,
or(neg(X2),and(neg(X3),or(neg(X),and(neg(X3),neg(neg(X3)))))) = or(neg(X2),and(neg(X3),or(neg(X),neg(or(X3,neg(X3)))))),
inference(congruence,[status(thm)],[c1776]) ).
cnf(c1778,plain,
and(and(neg(X3),X3),or(neg(X2),and(neg(X3),or(neg(X),and(neg(X3),neg(neg(X3))))))) = and(and(neg(X3),X3),or(neg(X2),and(neg(X3),or(neg(X),neg(or(X3,neg(X3))))))),
inference(congruence,[status(thm)],[c1777]) ).
cnf(c1779,plain,
f(X,or(X2,neg(X2))) = or(neg(X),neg(or(X2,neg(X2)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1780,plain,
or(neg(X),neg(or(X2,neg(X2)))) = f(X,or(X2,neg(X2))),
inference(symmetry,[status(thm)],[c1779]) ).
cnf(c1781,plain,
and(neg(X2),or(neg(X),neg(or(X2,neg(X2))))) = and(neg(X2),f(X,or(X2,neg(X2)))),
inference(congruence,[status(thm)],[c1780]) ).
cnf(c1782,plain,
or(neg(X2),and(neg(X3),or(neg(X),neg(or(X3,neg(X3)))))) = or(neg(X2),and(neg(X3),f(X,or(X3,neg(X3))))),
inference(congruence,[status(thm)],[c1781]) ).
cnf(c1783,plain,
and(and(neg(X3),X3),or(neg(X2),and(neg(X3),or(neg(X),neg(or(X3,neg(X3))))))) = and(and(neg(X3),X3),or(neg(X2),and(neg(X3),f(X,or(X3,neg(X3)))))),
inference(congruence,[status(thm)],[c1782]) ).
cnf(c1784,plain,
neg(and(X,or(X2,neg(X2)))) = f(X,or(X2,neg(X2))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1785,plain,
f(X,or(X2,neg(X2))) = neg(and(X,or(X2,neg(X2)))),
inference(symmetry,[status(thm)],[c1784]) ).
cnf(c1786,plain,
and(neg(X2),f(X,or(X2,neg(X2)))) = and(neg(X2),neg(and(X,or(X2,neg(X2))))),
inference(congruence,[status(thm)],[c1785]) ).
cnf(c1787,plain,
or(neg(X2),and(neg(X3),f(X,or(X3,neg(X3))))) = or(neg(X2),and(neg(X3),neg(and(X,or(X3,neg(X3)))))),
inference(congruence,[status(thm)],[c1786]) ).
cnf(c1788,plain,
and(and(neg(X3),X3),or(neg(X2),and(neg(X3),f(X,or(X3,neg(X3)))))) = and(and(neg(X3),X3),or(neg(X2),and(neg(X3),neg(and(X,or(X3,neg(X3))))))),
inference(congruence,[status(thm)],[c1787]) ).
cnf(c1789,plain,
neg(or(X2,and(X,or(X2,neg(X2))))) = and(neg(X2),neg(and(X,or(X2,neg(X2))))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1790,plain,
and(neg(X2),neg(and(X,or(X2,neg(X2))))) = neg(or(X2,and(X,or(X2,neg(X2))))),
inference(symmetry,[status(thm)],[c1789]) ).
cnf(c1791,plain,
or(neg(X2),and(neg(X3),neg(and(X,or(X3,neg(X3)))))) = or(neg(X2),neg(or(X3,and(X,or(X3,neg(X3)))))),
inference(congruence,[status(thm)],[c1790]) ).
cnf(c1792,plain,
and(and(neg(X3),X3),or(neg(X2),and(neg(X3),neg(and(X,or(X3,neg(X3))))))) = and(and(neg(X3),X3),or(neg(X2),neg(or(X3,and(X,or(X3,neg(X3))))))),
inference(congruence,[status(thm)],[c1791]) ).
cnf(c1793,plain,
f(X2,or(X3,and(X,or(X3,neg(X3))))) = or(neg(X2),neg(or(X3,and(X,or(X3,neg(X3)))))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1794,plain,
or(neg(X2),neg(or(X3,and(X,or(X3,neg(X3)))))) = f(X2,or(X3,and(X,or(X3,neg(X3))))),
inference(symmetry,[status(thm)],[c1793]) ).
cnf(c1795,plain,
and(and(neg(X3),X3),or(neg(X2),neg(or(X3,and(X,or(X3,neg(X3))))))) = and(and(neg(X3),X3),f(X2,or(X3,and(X,or(X3,neg(X3)))))),
inference(congruence,[status(thm)],[c1794]) ).
cnf(c1796,plain,
neg(and(X2,or(X3,and(X,or(X3,neg(X3)))))) = f(X2,or(X3,and(X,or(X3,neg(X3))))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1797,plain,
f(X2,or(X3,and(X,or(X3,neg(X3))))) = neg(and(X2,or(X3,and(X,or(X3,neg(X3)))))),
inference(symmetry,[status(thm)],[c1796]) ).
cnf(c1798,plain,
and(and(neg(X3),X3),f(X2,or(X3,and(X,or(X3,neg(X3)))))) = and(and(neg(X3),X3),neg(and(X2,or(X3,and(X,or(X3,neg(X3))))))),
inference(congruence,[status(thm)],[c1797]) ).
cnf(c1799,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1800,plain,
and(neg(X),X) = and(neg(X),neg(neg(X))),
inference(congruence,[status(thm)],[c1799]) ).
cnf(c1801,plain,
and(and(neg(X3),X3),neg(and(X2,or(X3,and(X,or(X3,neg(X3))))))) = and(and(neg(X3),neg(neg(X3))),neg(and(X2,or(X3,and(X,or(X3,neg(X3))))))),
inference(congruence,[status(thm)],[c1800]) ).
cnf(c1802,plain,
neg(or(X,neg(X))) = and(neg(X),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1803,plain,
and(neg(X),neg(neg(X))) = neg(or(X,neg(X))),
inference(symmetry,[status(thm)],[c1802]) ).
cnf(c1804,plain,
and(and(neg(X3),neg(neg(X3))),neg(and(X2,or(X3,and(X,or(X3,neg(X3))))))) = and(neg(or(X3,neg(X3))),neg(and(X2,or(X3,and(X,or(X3,neg(X3))))))),
inference(congruence,[status(thm)],[c1803]) ).
cnf(c1805,plain,
neg(or(or(X3,neg(X3)),and(X2,or(X3,and(X,or(X3,neg(X3))))))) = and(neg(or(X3,neg(X3))),neg(and(X2,or(X3,and(X,or(X3,neg(X3))))))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1806,plain,
and(neg(or(X3,neg(X3))),neg(and(X2,or(X3,and(X,or(X3,neg(X3))))))) = neg(or(or(X3,neg(X3)),and(X2,or(X3,and(X,or(X3,neg(X3))))))),
inference(symmetry,[status(thm)],[c1805]) ).
cnf(c1807,plain,
and(X,or(X2,neg(X2))) = and(or(X2,neg(X2)),X),
inference(substitution,[status(thm)],[c934]) ).
cnf(c1808,plain,
or(X2,and(X,or(X2,neg(X2)))) = or(X2,and(or(X2,neg(X2)),X)),
inference(congruence,[status(thm)],[c1807]) ).
cnf(c1809,plain,
and(X2,or(X3,and(X,or(X3,neg(X3))))) = and(X2,or(X3,and(or(X3,neg(X3)),X))),
inference(congruence,[status(thm)],[c1808]) ).
cnf(c1810,plain,
or(or(X3,neg(X3)),and(X2,or(X3,and(X,or(X3,neg(X3)))))) = or(or(X3,neg(X3)),and(X2,or(X3,and(or(X3,neg(X3)),X)))),
inference(congruence,[status(thm)],[c1809]) ).
cnf(c1811,plain,
and(X2,or(X3,and(or(X3,neg(X3)),X))) = and(or(X3,and(or(X3,neg(X3)),X)),X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c1812,plain,
or(or(X3,neg(X3)),and(X2,or(X3,and(or(X3,neg(X3)),X)))) = or(or(X3,neg(X3)),and(or(X3,and(or(X3,neg(X3)),X)),X2)),
inference(congruence,[status(thm)],[c1811]) ).
cnf(c1813,plain,
or(or(X3,neg(X3)),and(or(X3,and(or(X3,neg(X3)),X)),X2)) = or(and(or(X3,and(or(X3,neg(X3)),X)),X2),or(X3,neg(X3))),
inference(substitution,[status(thm)],[c913]) ).
cnf(c1814,plain,
and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))) = or(X2,neg(X2)),
inference(substitution,[status(thm)],[c1110]) ).
cnf(c1815,plain,
or(X2,neg(X2)) = and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))),
inference(symmetry,[status(thm)],[c1814]) ).
cnf(c1816,plain,
or(and(or(X3,and(or(X3,neg(X3)),X)),X2),or(X3,neg(X3))) = or(and(or(X3,and(or(X3,neg(X3)),X)),X2),and(or(X3,neg(X3)),or(or(X3,neg(X3)),neg(X)))),
inference(congruence,[status(thm)],[c1815]) ).
cnf(c1817,plain,
and(X,or(X,neg(X))) = X,
inference(substitution,[status(thm)],[c1110]) ).
cnf(c1818,plain,
X = and(X,or(X,neg(X))),
inference(symmetry,[status(thm)],[c1817]) ).
cnf(c1819,plain,
or(X2,and(or(X2,neg(X2)),X)) = or(and(X2,or(X2,neg(X2))),and(or(X2,neg(X2)),X)),
inference(congruence,[status(thm)],[c1818]) ).
cnf(c1820,plain,
and(or(X3,and(or(X3,neg(X3)),X)),X2) = and(or(and(X3,or(X3,neg(X3))),and(or(X3,neg(X3)),X)),X2),
inference(congruence,[status(thm)],[c1819]) ).
cnf(c1821,plain,
or(and(or(X3,and(or(X3,neg(X3)),X)),X2),and(or(X3,neg(X3)),or(or(X3,neg(X3)),neg(X)))) = or(and(or(and(X3,or(X3,neg(X3))),and(or(X3,neg(X3)),X)),X2),and(or(X3,neg(X3)),or(or(X3,neg(X3)),neg(X)))),
inference(congruence,[status(thm)],[c1820]) ).
cnf(c1822,plain,
and(or(X,neg(X)),or(X,neg(X))) = or(X,neg(X)),
inference(substitution,[status(thm)],[c1220]) ).
cnf(c1823,plain,
or(X,neg(X)) = and(or(X,neg(X)),or(X,neg(X))),
inference(symmetry,[status(thm)],[c1822]) ).
cnf(c1824,plain,
or(or(X2,neg(X2)),neg(X)) = or(and(or(X2,neg(X2)),or(X2,neg(X2))),neg(X)),
inference(congruence,[status(thm)],[c1823]) ).
cnf(c1825,plain,
and(or(X2,neg(X2)),or(or(X2,neg(X2)),neg(X))) = and(or(X2,neg(X2)),or(and(or(X2,neg(X2)),or(X2,neg(X2))),neg(X))),
inference(congruence,[status(thm)],[c1824]) ).
cnf(c1826,plain,
or(and(or(and(X3,or(X3,neg(X3))),and(or(X3,neg(X3)),X)),X2),and(or(X3,neg(X3)),or(or(X3,neg(X3)),neg(X)))) = or(and(or(and(X3,or(X3,neg(X3))),and(or(X3,neg(X3)),X)),X2),and(or(X3,neg(X3)),or(and(or(X3,neg(X3)),or(X3,neg(X3))),neg(X)))),
inference(congruence,[status(thm)],[c1825]) ).
cnf(c1827,plain,
or(and(or(and(X3,or(X3,neg(X3))),and(or(X3,neg(X3)),X)),X2),and(or(X3,neg(X3)),or(and(or(X3,neg(X3)),or(X3,neg(X3))),neg(X)))) = or(X3,neg(X3)),
inference(substitution,[status(thm)],[c1276]) ).
cnf(c1828,plain,
or(and(or(and(X3,or(X3,neg(X3))),and(or(X3,neg(X3)),X)),X2),and(or(X3,neg(X3)),or(or(X3,neg(X3)),neg(X)))) = or(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1826,c1827]) ).
cnf(c1829,plain,
or(and(or(X3,and(or(X3,neg(X3)),X)),X2),and(or(X3,neg(X3)),or(or(X3,neg(X3)),neg(X)))) = or(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1821,c1828]) ).
cnf(c1830,plain,
or(and(or(X3,and(or(X3,neg(X3)),X)),X2),or(X3,neg(X3))) = or(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1816,c1829]) ).
cnf(c1831,plain,
or(or(X3,neg(X3)),and(or(X3,and(or(X3,neg(X3)),X)),X2)) = or(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1813,c1830]) ).
cnf(c1832,plain,
or(or(X3,neg(X3)),and(X2,or(X3,and(or(X3,neg(X3)),X)))) = or(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1812,c1831]) ).
cnf(c1833,plain,
or(or(X3,neg(X3)),and(X2,or(X3,and(X,or(X3,neg(X3)))))) = or(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1810,c1832]) ).
cnf(c1834,plain,
neg(or(or(X3,neg(X3)),and(X2,or(X3,and(X,or(X3,neg(X3))))))) = neg(or(X3,neg(X3))),
inference(congruence,[status(thm)],[c1833]) ).
cnf(c1835,plain,
neg(or(X,neg(X))) = and(neg(X),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1836,plain,
and(neg(X),neg(neg(X))) = and(neg(X),X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c1837,plain,
and(neg(X),X) = and(X,neg(X)),
inference(substitution,[status(thm)],[c930]) ).
cnf(c1838,plain,
and(neg(X),neg(neg(X))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c1836,c1837]) ).
cnf(c1839,plain,
neg(or(X,neg(X))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c1835,c1838]) ).
cnf(c1840,plain,
neg(or(or(X3,neg(X3)),and(X2,or(X3,and(X,or(X3,neg(X3))))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1834,c1839]) ).
cnf(c1841,plain,
and(neg(or(X3,neg(X3))),neg(and(X2,or(X3,and(X,or(X3,neg(X3))))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1806,c1840]) ).
cnf(c1842,plain,
and(and(neg(X3),neg(neg(X3))),neg(and(X2,or(X3,and(X,or(X3,neg(X3))))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1804,c1841]) ).
cnf(c1843,plain,
and(and(neg(X3),X3),neg(and(X2,or(X3,and(X,or(X3,neg(X3))))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1801,c1842]) ).
cnf(c1844,plain,
and(and(neg(X3),X3),f(X2,or(X3,and(X,or(X3,neg(X3)))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1798,c1843]) ).
cnf(c1845,plain,
and(and(neg(X3),X3),or(neg(X2),neg(or(X3,and(X,or(X3,neg(X3))))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1795,c1844]) ).
cnf(c1846,plain,
and(and(neg(X3),X3),or(neg(X2),and(neg(X3),neg(and(X,or(X3,neg(X3))))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1792,c1845]) ).
cnf(c1847,plain,
and(and(neg(X3),X3),or(neg(X2),and(neg(X3),f(X,or(X3,neg(X3)))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1788,c1846]) ).
cnf(c1848,plain,
and(and(neg(X3),X3),or(neg(X2),and(neg(X3),or(neg(X),neg(or(X3,neg(X3))))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1783,c1847]) ).
cnf(c1849,plain,
and(and(neg(X3),X3),or(neg(X2),and(neg(X3),or(neg(X),and(neg(X3),neg(neg(X3))))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1778,c1848]) ).
cnf(c1850,plain,
and(and(neg(X3),X3),or(neg(X2),and(neg(X3),or(neg(X),and(neg(X3),X3))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1772,c1849]) ).
cnf(c1851,plain,
and(and(neg(X3),X3),or(neg(X2),and(neg(X3),or(neg(X),and(X3,neg(X3)))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1766,c1850]) ).
cnf(c1852,plain,
and(and(X3,neg(X3)),or(neg(X2),and(neg(X3),or(neg(X),and(X3,neg(X3)))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1760,c1851]) ).
cnf(c1853,plain,
and(and(X3,neg(X3)),or(neg(neg(X2)),and(neg(X3),or(neg(X),and(X3,neg(X3)))))) = and(X3,neg(X3)),
inference(substitution,[status(thm)],[c1852]) ).
cnf(c1854,plain,
and(and(X3,neg(X3)),or(X2,and(neg(X3),or(neg(X),and(X3,neg(X3)))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1757,c1853]) ).
cnf(c1855,plain,
and(and(X3,neg(X3)),or(X2,and(neg(X3),or(neg(neg(X)),and(X3,neg(X3)))))) = and(X3,neg(X3)),
inference(substitution,[status(thm)],[c1854]) ).
cnf(c1856,plain,
and(and(X3,neg(X3)),or(X2,and(neg(X3),or(X,and(X3,neg(X3)))))) = and(X3,neg(X3)),
inference(transitivity,[status(thm)],[c1754,c1855]) ).
cnf(c1857,plain,
and(and(X,neg(X)),or(X2,and(neg(X),or(or(X,neg(X)),and(X,neg(X)))))) = and(X,neg(X)),
inference(substitution,[status(thm)],[c1856]) ).
cnf(c1858,plain,
and(and(X,neg(X)),or(X2,neg(X))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c1749,c1857]) ).
cnf(c1859,plain,
and(or(X2,neg(X)),and(X,neg(X))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c1679,c1858]) ).
cnf(c1860,plain,
and(or(X,neg(X)),and(X,neg(X))) = and(X,neg(X)),
inference(substitution,[status(thm)],[c1859]) ).
cnf(c1861,plain,
or(and(X2,and(X,neg(X))),and(or(X,neg(X)),and(X,neg(X)))) = or(and(X2,and(X,neg(X))),and(X,neg(X))),
inference(congruence,[status(thm)],[c1860]) ).
cnf(c1862,plain,
or(and(X2,and(X,neg(X))),and(X,neg(X))) = and(X,neg(X)),
inference(substitution,[status(thm)],[c1209]) ).
cnf(c1863,plain,
or(and(X2,and(X,neg(X))),and(or(X,neg(X)),and(X,neg(X)))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c1861,c1862]) ).
cnf(c1864,plain,
and(X2,and(X,neg(X))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c1678,c1863]) ).
cnf(c1865,plain,
and(X,neg(X)) = and(X2,and(X,neg(X))),
inference(symmetry,[status(thm)],[c1864]) ).
cnf(c1866,plain,
or(and(X2,neg(X2)),and(X3,or(neg(X3),and(X3,or(X,neg(X)))))) = or(and(X3,and(X2,neg(X2))),and(X3,or(neg(X3),and(X3,or(X,neg(X)))))),
inference(congruence,[status(thm)],[c1865]) ).
cnf(c1867,plain,
or(and(X3,and(X2,neg(X2))),and(X3,or(neg(X3),and(X3,or(X,neg(X)))))) = X3,
inference(substitution,[status(thm)],[c1280]) ).
cnf(c1868,plain,
or(and(X2,neg(X2)),and(X3,or(neg(X3),and(X3,or(X,neg(X)))))) = X3,
inference(transitivity,[status(thm)],[c1866,c1867]) ).
cnf(c1869,plain,
or(and(X,neg(X)),X2) = X2,
inference(transitivity,[status(thm)],[c1284,c1868]) ).
cnf(c1870,plain,
or(X2,and(X,neg(X))) = X2,
inference(transitivity,[status(thm)],[c1114,c1869]) ).
cnf(c1871,plain,
or(or(X,neg(X)),and(neg(X),neg(neg(X)))) = or(X,neg(X)),
inference(substitution,[status(thm)],[c1870]) ).
cnf(c1872,plain,
or(X,neg(X)) = or(or(X,neg(X)),and(neg(X),neg(neg(X)))),
inference(symmetry,[status(thm)],[c1871]) ).
cnf(c1873,plain,
and(X2,or(X,neg(X))) = and(X2,or(or(X,neg(X)),and(neg(X),neg(neg(X))))),
inference(congruence,[status(thm)],[c1872]) ).
cnf(c1874,plain,
and(X2,and(neg(X),neg(neg(X)))) = and(neg(X),neg(neg(X))),
inference(substitution,[status(thm)],[c1864]) ).
cnf(c1875,plain,
and(neg(X),neg(neg(X))) = and(X2,and(neg(X),neg(neg(X)))),
inference(symmetry,[status(thm)],[c1874]) ).
cnf(c1876,plain,
or(or(X,neg(X)),and(neg(X),neg(neg(X)))) = or(or(X,neg(X)),and(X2,and(neg(X),neg(neg(X))))),
inference(congruence,[status(thm)],[c1875]) ).
cnf(c1877,plain,
and(X2,or(or(X,neg(X)),and(neg(X),neg(neg(X))))) = and(X2,or(or(X,neg(X)),and(X2,and(neg(X),neg(neg(X)))))),
inference(congruence,[status(thm)],[c1876]) ).
cnf(c1878,plain,
neg(or(X,neg(X))) = and(neg(X),neg(neg(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1879,plain,
and(neg(X),neg(neg(X))) = neg(or(X,neg(X))),
inference(symmetry,[status(thm)],[c1878]) ).
cnf(c1880,plain,
and(X2,and(neg(X),neg(neg(X)))) = and(X2,neg(or(X,neg(X)))),
inference(congruence,[status(thm)],[c1879]) ).
cnf(c1881,plain,
or(or(X,neg(X)),and(X2,and(neg(X),neg(neg(X))))) = or(or(X,neg(X)),and(X2,neg(or(X,neg(X))))),
inference(congruence,[status(thm)],[c1880]) ).
cnf(c1882,plain,
and(X2,or(or(X,neg(X)),and(X2,and(neg(X),neg(neg(X)))))) = and(X2,or(or(X,neg(X)),and(X2,neg(or(X,neg(X)))))),
inference(congruence,[status(thm)],[c1881]) ).
cnf(c1883,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1884,plain,
and(X2,or(or(X,neg(X)),and(X2,neg(or(X,neg(X)))))) = and(neg(neg(X2)),or(or(X,neg(X)),and(X2,neg(or(X,neg(X)))))),
inference(congruence,[status(thm)],[c1883]) ).
cnf(c1885,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c1886,plain,
and(X2,neg(or(X,neg(X)))) = and(neg(neg(X2)),neg(or(X,neg(X)))),
inference(congruence,[status(thm)],[c1885]) ).
cnf(c1887,plain,
or(or(X,neg(X)),and(X2,neg(or(X,neg(X))))) = or(or(X,neg(X)),and(neg(neg(X2)),neg(or(X,neg(X))))),
inference(congruence,[status(thm)],[c1886]) ).
cnf(c1888,plain,
and(neg(neg(X2)),or(or(X,neg(X)),and(X2,neg(or(X,neg(X)))))) = and(neg(neg(X2)),or(or(X,neg(X)),and(neg(neg(X2)),neg(or(X,neg(X)))))),
inference(congruence,[status(thm)],[c1887]) ).
cnf(c1889,plain,
or(X,neg(X)) = or(neg(X),X),
inference(substitution,[status(thm)],[c913]) ).
cnf(c1890,plain,
or(neg(X2),or(X,neg(X))) = or(neg(X2),or(neg(X),X)),
inference(congruence,[status(thm)],[c1889]) ).
cnf(c1891,plain,
f(X,neg(X)) = or(neg(X),X),
inference(substitution,[status(thm)],[c85]) ).
cnf(c1892,plain,
or(neg(X),X) = f(X,neg(X)),
inference(symmetry,[status(thm)],[c1891]) ).
cnf(c1893,plain,
or(neg(X2),or(neg(X),X)) = or(neg(X2),f(X,neg(X))),
inference(congruence,[status(thm)],[c1892]) ).
cnf(c1894,plain,
neg(and(X,neg(X))) = f(X,neg(X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1895,plain,
f(X,neg(X)) = neg(and(X,neg(X))),
inference(symmetry,[status(thm)],[c1894]) ).
cnf(c1896,plain,
or(neg(X2),f(X,neg(X))) = or(neg(X2),neg(and(X,neg(X)))),
inference(congruence,[status(thm)],[c1895]) ).
cnf(c1897,plain,
and(X2,X) = and(X,X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c1898,plain,
neg(and(X2,X)) = neg(and(X,X2)),
inference(congruence,[status(thm)],[c1897]) ).
cnf(c1899,plain,
neg(f(X,X2)) = and(X,X2),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1900,plain,
and(X,X2) = neg(f(X,X2)),
inference(symmetry,[status(thm)],[c1899]) ).
cnf(c1901,plain,
neg(and(X,X2)) = neg(neg(f(X,X2))),
inference(congruence,[status(thm)],[c1900]) ).
cnf(c1902,plain,
neg(neg(f(X,X2))) = f(X,X2),
inference(substitution,[status(thm)],[c79]) ).
cnf(c1903,plain,
f(X,X2) = or(neg(X),neg(X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1904,plain,
or(neg(X2),neg(X)) = or(neg(X),neg(X2)),
inference(substitution,[status(thm)],[c913]) ).
cnf(c1905,plain,
or(neg(X),neg(X2)) = or(neg(X2),neg(X)),
inference(symmetry,[status(thm)],[c1904]) ).
cnf(c1906,plain,
f(X,X2) = or(neg(X2),neg(X)),
inference(transitivity,[status(thm)],[c1903,c1905]) ).
cnf(c1907,plain,
neg(neg(f(X,X2))) = or(neg(X2),neg(X)),
inference(transitivity,[status(thm)],[c1902,c1906]) ).
cnf(c1908,plain,
neg(and(X,X2)) = or(neg(X2),neg(X)),
inference(transitivity,[status(thm)],[c1901,c1907]) ).
cnf(c1909,plain,
neg(and(X2,X)) = or(neg(X2),neg(X)),
inference(transitivity,[status(thm)],[c1898,c1908]) ).
cnf(c1910,plain,
neg(and(X2,and(X,neg(X)))) = or(neg(X2),neg(and(X,neg(X)))),
inference(substitution,[status(thm)],[c1909]) ).
cnf(c1911,plain,
or(neg(X2),neg(and(X,neg(X)))) = neg(and(X2,and(X,neg(X)))),
inference(symmetry,[status(thm)],[c1910]) ).
cnf(c1912,plain,
neg(and(X2,and(X,neg(X)))) = neg(and(X,neg(X))),
inference(congruence,[status(thm)],[c1864]) ).
cnf(c1913,plain,
neg(and(X,neg(X))) = f(X,neg(X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1914,plain,
f(X,neg(X)) = or(neg(X),X),
inference(substitution,[status(thm)],[c85]) ).
cnf(c1915,plain,
or(X,neg(X)) = or(neg(X),X),
inference(substitution,[status(thm)],[c913]) ).
cnf(c1916,plain,
or(neg(X),X) = or(X,neg(X)),
inference(symmetry,[status(thm)],[c1915]) ).
cnf(c1917,plain,
f(X,neg(X)) = or(X,neg(X)),
inference(transitivity,[status(thm)],[c1914,c1916]) ).
cnf(c1918,plain,
neg(and(X,neg(X))) = or(X,neg(X)),
inference(transitivity,[status(thm)],[c1913,c1917]) ).
cnf(c1919,plain,
neg(and(X2,and(X,neg(X)))) = or(X,neg(X)),
inference(transitivity,[status(thm)],[c1912,c1918]) ).
cnf(c1920,plain,
or(neg(X2),neg(and(X,neg(X)))) = or(X,neg(X)),
inference(transitivity,[status(thm)],[c1911,c1919]) ).
cnf(c1921,plain,
or(neg(X2),f(X,neg(X))) = or(X,neg(X)),
inference(transitivity,[status(thm)],[c1896,c1920]) ).
cnf(c1922,plain,
or(neg(X2),or(neg(X),X)) = or(X,neg(X)),
inference(transitivity,[status(thm)],[c1893,c1921]) ).
cnf(c1923,plain,
or(neg(X2),or(X,neg(X))) = or(X,neg(X)),
inference(transitivity,[status(thm)],[c1890,c1922]) ).
cnf(c1924,plain,
or(X,neg(X)) = or(neg(X2),or(X,neg(X))),
inference(symmetry,[status(thm)],[c1923]) ).
cnf(c1925,plain,
or(or(X,neg(X)),and(neg(neg(X2)),neg(or(X,neg(X))))) = or(or(neg(X2),or(X,neg(X))),and(neg(neg(X2)),neg(or(X,neg(X))))),
inference(congruence,[status(thm)],[c1924]) ).
cnf(c1926,plain,
and(neg(neg(X2)),or(or(X,neg(X)),and(neg(neg(X2)),neg(or(X,neg(X)))))) = and(neg(neg(X2)),or(or(neg(X2),or(X,neg(X))),and(neg(neg(X2)),neg(or(X,neg(X)))))),
inference(congruence,[status(thm)],[c1925]) ).
cnf(c1927,plain,
or(or(X2,X),and(neg(X2),neg(X))) = or(and(neg(X2),neg(X)),or(X2,X)),
inference(substitution,[status(thm)],[c913]) ).
cnf(c1928,plain,
and(neg(X2),or(or(X2,X),and(neg(X2),neg(X)))) = and(neg(X2),or(and(neg(X2),neg(X)),or(X2,X))),
inference(congruence,[status(thm)],[c1927]) ).
cnf(c1929,plain,
and(neg(X2),or(and(neg(X2),neg(X)),or(X2,X))) = and(or(and(neg(X2),neg(X)),or(X2,X)),neg(X2)),
inference(substitution,[status(thm)],[c930]) ).
cnf(c1930,plain,
or(X2,X) = f(neg(X2),neg(X)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c1931,plain,
or(and(neg(X2),neg(X)),or(X2,X)) = or(and(neg(X2),neg(X)),f(neg(X2),neg(X))),
inference(congruence,[status(thm)],[c1930]) ).
cnf(c1932,plain,
and(neg(X2),or(and(neg(X2),neg(X)),or(X2,X))) = and(neg(X2),or(and(neg(X2),neg(X)),f(neg(X2),neg(X)))),
inference(congruence,[status(thm)],[c1931]) ).
cnf(c1933,plain,
or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),or(X2,X)))) = or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),f(neg(X2),neg(X))))),
inference(congruence,[status(thm)],[c1932]) ).
cnf(c1934,plain,
neg(and(neg(X2),neg(X))) = f(neg(X2),neg(X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1935,plain,
f(neg(X2),neg(X)) = neg(and(neg(X2),neg(X))),
inference(symmetry,[status(thm)],[c1934]) ).
cnf(c1936,plain,
or(and(neg(X2),neg(X)),f(neg(X2),neg(X))) = or(and(neg(X2),neg(X)),neg(and(neg(X2),neg(X)))),
inference(congruence,[status(thm)],[c1935]) ).
cnf(c1937,plain,
and(neg(X2),or(and(neg(X2),neg(X)),f(neg(X2),neg(X)))) = and(neg(X2),or(and(neg(X2),neg(X)),neg(and(neg(X2),neg(X))))),
inference(congruence,[status(thm)],[c1936]) ).
cnf(c1938,plain,
or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),f(neg(X2),neg(X))))) = or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),neg(and(neg(X2),neg(X)))))),
inference(congruence,[status(thm)],[c1937]) ).
cnf(c1939,plain,
and(neg(X2),neg(X)) = neg(or(X2,X)),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c1940,plain,
or(and(neg(X2),neg(X)),neg(and(neg(X2),neg(X)))) = or(neg(or(X2,X)),neg(and(neg(X2),neg(X)))),
inference(congruence,[status(thm)],[c1939]) ).
cnf(c1941,plain,
and(neg(X2),or(and(neg(X2),neg(X)),neg(and(neg(X2),neg(X))))) = and(neg(X2),or(neg(or(X2,X)),neg(and(neg(X2),neg(X))))),
inference(congruence,[status(thm)],[c1940]) ).
cnf(c1942,plain,
or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),neg(and(neg(X2),neg(X)))))) = or(and(neg(X2),neg(X)),and(neg(X2),or(neg(or(X2,X)),neg(and(neg(X2),neg(X)))))),
inference(congruence,[status(thm)],[c1941]) ).
cnf(c1943,plain,
f(or(X2,X),and(neg(X2),neg(X))) = or(neg(or(X2,X)),neg(and(neg(X2),neg(X)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1944,plain,
or(neg(or(X2,X)),neg(and(neg(X2),neg(X)))) = f(or(X2,X),and(neg(X2),neg(X))),
inference(symmetry,[status(thm)],[c1943]) ).
cnf(c1945,plain,
and(neg(X2),or(neg(or(X2,X)),neg(and(neg(X2),neg(X))))) = and(neg(X2),f(or(X2,X),and(neg(X2),neg(X)))),
inference(congruence,[status(thm)],[c1944]) ).
cnf(c1946,plain,
or(and(neg(X2),neg(X)),and(neg(X2),or(neg(or(X2,X)),neg(and(neg(X2),neg(X)))))) = or(and(neg(X2),neg(X)),and(neg(X2),f(or(X2,X),and(neg(X2),neg(X))))),
inference(congruence,[status(thm)],[c1945]) ).
cnf(c1947,plain,
neg(and(or(X2,X),and(neg(X2),neg(X)))) = f(or(X2,X),and(neg(X2),neg(X))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1948,plain,
f(or(X2,X),and(neg(X2),neg(X))) = neg(and(or(X2,X),and(neg(X2),neg(X)))),
inference(symmetry,[status(thm)],[c1947]) ).
cnf(c1949,plain,
and(neg(X2),f(or(X2,X),and(neg(X2),neg(X)))) = and(neg(X2),neg(and(or(X2,X),and(neg(X2),neg(X))))),
inference(congruence,[status(thm)],[c1948]) ).
cnf(c1950,plain,
or(and(neg(X2),neg(X)),and(neg(X2),f(or(X2,X),and(neg(X2),neg(X))))) = or(and(neg(X2),neg(X)),and(neg(X2),neg(and(or(X2,X),and(neg(X2),neg(X)))))),
inference(congruence,[status(thm)],[c1949]) ).
cnf(c1951,plain,
neg(or(X2,and(or(X2,X),and(neg(X2),neg(X))))) = and(neg(X2),neg(and(or(X2,X),and(neg(X2),neg(X))))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1952,plain,
and(neg(X2),neg(and(or(X2,X),and(neg(X2),neg(X))))) = neg(or(X2,and(or(X2,X),and(neg(X2),neg(X))))),
inference(symmetry,[status(thm)],[c1951]) ).
cnf(c1953,plain,
or(and(neg(X2),neg(X)),and(neg(X2),neg(and(or(X2,X),and(neg(X2),neg(X)))))) = or(and(neg(X2),neg(X)),neg(or(X2,and(or(X2,X),and(neg(X2),neg(X)))))),
inference(congruence,[status(thm)],[c1952]) ).
cnf(c1954,plain,
and(neg(X2),neg(X)) = neg(or(X2,X)),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c1955,plain,
or(and(neg(X2),neg(X)),neg(or(X2,and(or(X2,X),and(neg(X2),neg(X)))))) = or(neg(or(X2,X)),neg(or(X2,and(or(X2,X),and(neg(X2),neg(X)))))),
inference(congruence,[status(thm)],[c1954]) ).
cnf(c1956,plain,
f(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X))))) = or(neg(or(X2,X)),neg(or(X2,and(or(X2,X),and(neg(X2),neg(X)))))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c1957,plain,
or(neg(or(X2,X)),neg(or(X2,and(or(X2,X),and(neg(X2),neg(X)))))) = f(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X))))),
inference(symmetry,[status(thm)],[c1956]) ).
cnf(c1958,plain,
neg(and(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X)))))) = f(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X))))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c1959,plain,
f(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X))))) = neg(and(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X)))))),
inference(symmetry,[status(thm)],[c1958]) ).
cnf(c1960,plain,
neg(and(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X)))))) = neg(X2),
inference(congruence,[status(thm)],[c358]) ).
cnf(c1961,plain,
f(or(X2,X),or(X2,and(or(X2,X),and(neg(X2),neg(X))))) = neg(X2),
inference(transitivity,[status(thm)],[c1959,c1960]) ).
cnf(c1962,plain,
or(neg(or(X2,X)),neg(or(X2,and(or(X2,X),and(neg(X2),neg(X)))))) = neg(X2),
inference(transitivity,[status(thm)],[c1957,c1961]) ).
cnf(c1963,plain,
or(and(neg(X2),neg(X)),neg(or(X2,and(or(X2,X),and(neg(X2),neg(X)))))) = neg(X2),
inference(transitivity,[status(thm)],[c1955,c1962]) ).
cnf(c1964,plain,
or(and(neg(X2),neg(X)),and(neg(X2),neg(and(or(X2,X),and(neg(X2),neg(X)))))) = neg(X2),
inference(transitivity,[status(thm)],[c1953,c1963]) ).
cnf(c1965,plain,
or(and(neg(X2),neg(X)),and(neg(X2),f(or(X2,X),and(neg(X2),neg(X))))) = neg(X2),
inference(transitivity,[status(thm)],[c1950,c1964]) ).
cnf(c1966,plain,
or(and(neg(X2),neg(X)),and(neg(X2),or(neg(or(X2,X)),neg(and(neg(X2),neg(X)))))) = neg(X2),
inference(transitivity,[status(thm)],[c1946,c1965]) ).
cnf(c1967,plain,
or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),neg(and(neg(X2),neg(X)))))) = neg(X2),
inference(transitivity,[status(thm)],[c1942,c1966]) ).
cnf(c1968,plain,
or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),f(neg(X2),neg(X))))) = neg(X2),
inference(transitivity,[status(thm)],[c1938,c1967]) ).
cnf(c1969,plain,
or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),or(X2,X)))) = neg(X2),
inference(transitivity,[status(thm)],[c1933,c1968]) ).
cnf(c1970,plain,
neg(X2) = or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),or(X2,X)))),
inference(symmetry,[status(thm)],[c1969]) ).
cnf(c1971,plain,
and(or(and(neg(X2),neg(X)),or(X2,X)),neg(X2)) = and(or(and(neg(X2),neg(X)),or(X2,X)),or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),or(X2,X))))),
inference(congruence,[status(thm)],[c1970]) ).
cnf(c1972,plain,
and(or(and(neg(X2),neg(X)),or(X2,X)),or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),or(X2,X))))) = or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),or(X2,X)))),
inference(substitution,[status(thm)],[c1391]) ).
cnf(c1973,plain,
and(or(and(neg(X2),neg(X)),or(X2,X)),or(and(neg(X2),neg(X)),and(neg(X2),or(and(neg(X2),neg(X)),or(X2,X))))) = neg(X2),
inference(transitivity,[status(thm)],[c1972,c1969]) ).
cnf(c1974,plain,
and(or(and(neg(X2),neg(X)),or(X2,X)),neg(X2)) = neg(X2),
inference(transitivity,[status(thm)],[c1971,c1973]) ).
cnf(c1975,plain,
and(neg(X2),or(and(neg(X2),neg(X)),or(X2,X))) = neg(X2),
inference(transitivity,[status(thm)],[c1929,c1974]) ).
cnf(c1976,plain,
and(neg(X2),or(or(X2,X),and(neg(X2),neg(X)))) = neg(X2),
inference(transitivity,[status(thm)],[c1928,c1975]) ).
cnf(c1977,plain,
and(neg(neg(X2)),or(or(neg(X2),or(X,neg(X))),and(neg(neg(X2)),neg(or(X,neg(X)))))) = neg(neg(X2)),
inference(substitution,[status(thm)],[c1976]) ).
cnf(c1978,plain,
and(neg(neg(X2)),or(or(neg(X2),or(X,neg(X))),and(neg(neg(X2)),neg(or(X,neg(X)))))) = X2,
inference(transitivity,[status(thm)],[c1977,c79]) ).
cnf(c1979,plain,
and(neg(neg(X2)),or(or(X,neg(X)),and(neg(neg(X2)),neg(or(X,neg(X)))))) = X2,
inference(transitivity,[status(thm)],[c1926,c1978]) ).
cnf(c1980,plain,
and(neg(neg(X2)),or(or(X,neg(X)),and(X2,neg(or(X,neg(X)))))) = X2,
inference(transitivity,[status(thm)],[c1888,c1979]) ).
cnf(c1981,plain,
and(X2,or(or(X,neg(X)),and(X2,neg(or(X,neg(X)))))) = X2,
inference(transitivity,[status(thm)],[c1884,c1980]) ).
cnf(c1982,plain,
and(X2,or(or(X,neg(X)),and(X2,and(neg(X),neg(neg(X)))))) = X2,
inference(transitivity,[status(thm)],[c1882,c1981]) ).
cnf(c1983,plain,
and(X2,or(or(X,neg(X)),and(neg(X),neg(neg(X))))) = X2,
inference(transitivity,[status(thm)],[c1877,c1982]) ).
cnf(c1984,plain,
and(X2,or(X,neg(X))) = X2,
inference(transitivity,[status(thm)],[c1873,c1983]) ).
cnf(c1985,plain,
and(and(X2,X3),or(X,neg(X))) = and(X2,X3),
inference(substitution,[status(thm)],[c1984]) ).
cnf(c1986,plain,
and(X2,X3) = and(and(X2,X3),or(X,neg(X))),
inference(symmetry,[status(thm)],[c1985]) ).
cnf(c1987,plain,
or(and(X3,X4),neg(X2)) = or(and(and(X3,X4),or(X,neg(X))),neg(X2)),
inference(congruence,[status(thm)],[c1986]) ).
cnf(c1988,plain,
and(and(X3,X4),or(and(X3,X4),neg(X2))) = and(and(X3,X4),or(and(and(X3,X4),or(X,neg(X))),neg(X2))),
inference(congruence,[status(thm)],[c1987]) ).
cnf(c1989,plain,
or(and(and(and(X4,X5),X2),X3),and(and(X4,X5),or(and(X4,X5),neg(X2)))) = or(and(and(and(X4,X5),X2),X3),and(and(X4,X5),or(and(and(X4,X5),or(X,neg(X))),neg(X2)))),
inference(congruence,[status(thm)],[c1988]) ).
cnf(c1990,plain,
neg(and(X2,neg(X))) = or(neg(X2),neg(neg(X))),
inference(substitution,[status(thm)],[c1909]) ).
cnf(c1991,plain,
or(neg(X2),neg(neg(X))) = or(neg(X2),X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c1992,plain,
or(X,neg(X2)) = or(neg(X2),X),
inference(substitution,[status(thm)],[c913]) ).
cnf(c1993,plain,
or(neg(X2),X) = or(X,neg(X2)),
inference(symmetry,[status(thm)],[c1992]) ).
cnf(c1994,plain,
or(neg(X2),neg(neg(X))) = or(X,neg(X2)),
inference(transitivity,[status(thm)],[c1991,c1993]) ).
cnf(c1995,plain,
neg(and(X2,neg(X))) = or(X,neg(X2)),
inference(transitivity,[status(thm)],[c1990,c1994]) ).
cnf(c1996,plain,
neg(and(X,neg(X))) = or(X,neg(X)),
inference(substitution,[status(thm)],[c1995]) ).
cnf(c1997,plain,
or(X,neg(X)) = neg(and(X,neg(X))),
inference(symmetry,[status(thm)],[c1996]) ).
cnf(c1998,plain,
and(and(X2,X3),or(X,neg(X))) = and(and(X2,X3),neg(and(X,neg(X)))),
inference(congruence,[status(thm)],[c1997]) ).
cnf(c1999,plain,
or(and(and(X3,X4),or(X,neg(X))),neg(X2)) = or(and(and(X3,X4),neg(and(X,neg(X)))),neg(X2)),
inference(congruence,[status(thm)],[c1998]) ).
cnf(c2000,plain,
and(and(X3,X4),or(and(and(X3,X4),or(X,neg(X))),neg(X2))) = and(and(X3,X4),or(and(and(X3,X4),neg(and(X,neg(X)))),neg(X2))),
inference(congruence,[status(thm)],[c1999]) ).
cnf(c2001,plain,
or(and(and(and(X4,X5),X2),X3),and(and(X4,X5),or(and(and(X4,X5),or(X,neg(X))),neg(X2)))) = or(and(and(and(X4,X5),X2),X3),and(and(X4,X5),or(and(and(X4,X5),neg(and(X,neg(X)))),neg(X2)))),
inference(congruence,[status(thm)],[c2000]) ).
cnf(c2002,plain,
or(and(X2,neg(X2)),X) = or(X,and(X2,neg(X2))),
inference(substitution,[status(thm)],[c913]) ).
cnf(c2003,plain,
or(X,and(X2,neg(X2))) = X,
inference(substitution,[status(thm)],[c1870]) ).
cnf(c2004,plain,
or(and(X2,neg(X2)),X) = X,
inference(transitivity,[status(thm)],[c2002,c2003]) ).
cnf(c2005,plain,
or(and(X,neg(X)),neg(and(X,neg(X)))) = neg(and(X,neg(X))),
inference(substitution,[status(thm)],[c2004]) ).
cnf(c2006,plain,
neg(and(X,neg(X))) = or(and(X,neg(X)),neg(and(X,neg(X)))),
inference(symmetry,[status(thm)],[c2005]) ).
cnf(c2007,plain,
and(and(X2,X3),neg(and(X,neg(X)))) = and(and(X2,X3),or(and(X,neg(X)),neg(and(X,neg(X))))),
inference(congruence,[status(thm)],[c2006]) ).
cnf(c2008,plain,
or(and(and(X3,X4),neg(and(X,neg(X)))),neg(X2)) = or(and(and(X3,X4),or(and(X,neg(X)),neg(and(X,neg(X))))),neg(X2)),
inference(congruence,[status(thm)],[c2007]) ).
cnf(c2009,plain,
and(and(X3,X4),or(and(and(X3,X4),neg(and(X,neg(X)))),neg(X2))) = and(and(X3,X4),or(and(and(X3,X4),or(and(X,neg(X)),neg(and(X,neg(X))))),neg(X2))),
inference(congruence,[status(thm)],[c2008]) ).
cnf(c2010,plain,
or(and(and(and(X4,X5),X2),X3),and(and(X4,X5),or(and(and(X4,X5),neg(and(X,neg(X)))),neg(X2)))) = or(and(and(and(X4,X5),X2),X3),and(and(X4,X5),or(and(and(X4,X5),or(and(X,neg(X)),neg(and(X,neg(X))))),neg(X2)))),
inference(congruence,[status(thm)],[c2009]) ).
cnf(c2011,plain,
or(and(X4,neg(X4)),and(and(X2,X3),X)) = and(and(X2,X3),X),
inference(substitution,[status(thm)],[c2004]) ).
cnf(c2012,plain,
and(and(X3,X4),X2) = or(and(X,neg(X)),and(and(X3,X4),X2)),
inference(symmetry,[status(thm)],[c2011]) ).
cnf(c2013,plain,
and(and(and(X4,X5),X2),X3) = and(or(and(X,neg(X)),and(and(X4,X5),X2)),X3),
inference(congruence,[status(thm)],[c2012]) ).
cnf(c2014,plain,
or(and(and(and(X5,X6),X3),X4),and(and(X5,X6),or(and(and(X5,X6),or(and(X2,neg(X2)),neg(and(X2,neg(X2))))),neg(X3)))) = or(and(or(and(X,neg(X)),and(and(X5,X6),X3)),X4),and(and(X5,X6),or(and(and(X5,X6),or(and(X2,neg(X2)),neg(and(X2,neg(X2))))),neg(X3)))),
inference(congruence,[status(thm)],[c2013]) ).
cnf(c2015,plain,
or(and(X2,X),and(X2,X)) = and(X2,X),
inference(substitution,[status(thm)],[c1120]) ).
cnf(c2016,plain,
and(X2,X) = or(and(X2,X),and(X2,X)),
inference(symmetry,[status(thm)],[c2015]) ).
cnf(c2017,plain,
and(and(X3,neg(X3)),and(X2,X)) = and(and(X3,neg(X3)),or(and(X2,X),and(X2,X))),
inference(congruence,[status(thm)],[c2016]) ).
cnf(c2018,plain,
or(X,and(X2,neg(X2))) = X,
inference(substitution,[status(thm)],[c1870]) ).
cnf(c2019,plain,
X = or(X,and(X2,neg(X2))),
inference(symmetry,[status(thm)],[c2018]) ).
cnf(c2020,plain,
and(X2,X) = and(X2,or(X,and(X2,neg(X2)))),
inference(congruence,[status(thm)],[c2019]) ).
cnf(c2021,plain,
or(X3,and(X2,X)) = or(X3,and(X2,or(X,and(X2,neg(X2))))),
inference(congruence,[status(thm)],[c2020]) ).
cnf(c2022,plain,
and(and(X4,neg(X4)),or(X3,and(X2,X))) = and(and(X4,neg(X4)),or(X3,and(X2,or(X,and(X2,neg(X2)))))),
inference(congruence,[status(thm)],[c2021]) ).
cnf(c2023,plain,
and(and(X2,neg(X2)),X) = and(X,and(X2,neg(X2))),
inference(substitution,[status(thm)],[c934]) ).
cnf(c2024,plain,
X = or(and(X2,neg(X2)),X),
inference(symmetry,[status(thm)],[c2004]) ).
cnf(c2025,plain,
and(X,and(X2,neg(X2))) = and(or(and(X2,neg(X2)),X),and(X2,neg(X2))),
inference(congruence,[status(thm)],[c2024]) ).
cnf(c2026,plain,
and(or(and(X2,neg(X2)),X),and(X2,neg(X2))) = and(X2,neg(X2)),
inference(substitution,[status(thm)],[c525]) ).
cnf(c2027,plain,
and(X,and(X2,neg(X2))) = and(X2,neg(X2)),
inference(transitivity,[status(thm)],[c2025,c2026]) ).
cnf(c2028,plain,
and(and(X2,neg(X2)),X) = and(X2,neg(X2)),
inference(transitivity,[status(thm)],[c2023,c2027]) ).
cnf(c2029,plain,
and(and(X3,neg(X3)),and(X,and(X2,neg(X2)))) = and(X3,neg(X3)),
inference(substitution,[status(thm)],[c2028]) ).
cnf(c2030,plain,
and(X3,neg(X3)) = and(and(X3,neg(X3)),and(X,and(X2,neg(X2)))),
inference(symmetry,[status(thm)],[c2029]) ).
cnf(c2031,plain,
and(X,and(X2,neg(X2))) = and(X2,neg(X2)),
inference(substitution,[status(thm)],[c1864]) ).
cnf(c2032,plain,
and(and(X3,neg(X3)),and(X,and(X2,neg(X2)))) = and(and(X3,neg(X3)),and(X2,neg(X2))),
inference(congruence,[status(thm)],[c2031]) ).
cnf(c2033,plain,
and(and(X2,neg(X2)),and(X,neg(X))) = and(X,neg(X)),
inference(substitution,[status(thm)],[c1864]) ).
cnf(c2034,plain,
and(and(X3,neg(X3)),and(X,and(X2,neg(X2)))) = and(X2,neg(X2)),
inference(transitivity,[status(thm)],[c2032,c2033]) ).
cnf(c2035,plain,
and(X2,neg(X2)) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c2030,c2034]) ).
cnf(c2036,plain,
and(X,neg(X)) = and(X2,neg(X2)),
inference(substitution,[status(thm)],[c2035]) ).
cnf(c2037,plain,
and(X2,neg(X2)) = and(X,neg(X)),
inference(symmetry,[status(thm)],[c2036]) ).
cnf(c2038,plain,
and(and(X4,neg(X4)),or(X3,and(X2,or(X,and(X2,neg(X2)))))) = and(and(X2,neg(X2)),or(X3,and(X2,or(X,and(X2,neg(X2)))))),
inference(congruence,[status(thm)],[c2037]) ).
cnf(c2039,plain,
and(neg(X),X) = and(X,neg(X)),
inference(substitution,[status(thm)],[c930]) ).
cnf(c2040,plain,
and(X,neg(X)) = and(neg(X),X),
inference(symmetry,[status(thm)],[c2039]) ).
cnf(c2041,plain,
and(and(X2,neg(X2)),or(X3,and(X2,or(X,and(X2,neg(X2)))))) = and(and(neg(X2),X2),or(X3,and(X2,or(X,and(X2,neg(X2)))))),
inference(congruence,[status(thm)],[c2040]) ).
cnf(c2042,plain,
and(neg(X),X) = and(X,neg(X)),
inference(substitution,[status(thm)],[c930]) ).
cnf(c2043,plain,
and(X,neg(X)) = and(neg(X),X),
inference(symmetry,[status(thm)],[c2042]) ).
cnf(c2044,plain,
or(X,and(X2,neg(X2))) = or(X,and(neg(X2),X2)),
inference(congruence,[status(thm)],[c2043]) ).
cnf(c2045,plain,
and(X2,or(X,and(X2,neg(X2)))) = and(X2,or(X,and(neg(X2),X2))),
inference(congruence,[status(thm)],[c2044]) ).
cnf(c2046,plain,
or(X3,and(X2,or(X,and(X2,neg(X2))))) = or(X3,and(X2,or(X,and(neg(X2),X2)))),
inference(congruence,[status(thm)],[c2045]) ).
cnf(c2047,plain,
and(and(neg(X2),X2),or(X3,and(X2,or(X,and(X2,neg(X2)))))) = and(and(neg(X2),X2),or(X3,and(X2,or(X,and(neg(X2),X2))))),
inference(congruence,[status(thm)],[c2046]) ).
cnf(c2048,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c2049,plain,
and(X2,or(X,and(neg(X2),X2))) = and(neg(neg(X2)),or(X,and(neg(X2),X2))),
inference(congruence,[status(thm)],[c2048]) ).
cnf(c2050,plain,
or(X3,and(X2,or(X,and(neg(X2),X2)))) = or(X3,and(neg(neg(X2)),or(X,and(neg(X2),X2)))),
inference(congruence,[status(thm)],[c2049]) ).
cnf(c2051,plain,
and(and(neg(X2),X2),or(X3,and(X2,or(X,and(neg(X2),X2))))) = and(and(neg(X2),X2),or(X3,and(neg(neg(X2)),or(X,and(neg(X2),X2))))),
inference(congruence,[status(thm)],[c2050]) ).
cnf(c2052,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c2053,plain,
and(neg(X),X) = and(neg(X),neg(neg(X))),
inference(congruence,[status(thm)],[c2052]) ).
cnf(c2054,plain,
or(X,and(neg(X2),X2)) = or(X,and(neg(X2),neg(neg(X2)))),
inference(congruence,[status(thm)],[c2053]) ).
cnf(c2055,plain,
and(neg(neg(X2)),or(X,and(neg(X2),X2))) = and(neg(neg(X2)),or(X,and(neg(X2),neg(neg(X2))))),
inference(congruence,[status(thm)],[c2054]) ).
cnf(c2056,plain,
or(X3,and(neg(neg(X2)),or(X,and(neg(X2),X2)))) = or(X3,and(neg(neg(X2)),or(X,and(neg(X2),neg(neg(X2)))))),
inference(congruence,[status(thm)],[c2055]) ).
cnf(c2057,plain,
and(and(neg(X2),X2),or(X3,and(neg(neg(X2)),or(X,and(neg(X2),X2))))) = and(and(neg(X2),X2),or(X3,and(neg(neg(X2)),or(X,and(neg(X2),neg(neg(X2))))))),
inference(congruence,[status(thm)],[c2056]) ).
cnf(c2058,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c2059,plain,
and(neg(X),X) = and(neg(X),neg(neg(X))),
inference(congruence,[status(thm)],[c2058]) ).
cnf(c2060,plain,
and(and(neg(X2),X2),or(X3,and(neg(neg(X2)),or(X,and(neg(X2),neg(neg(X2))))))) = and(and(neg(X2),neg(neg(X2))),or(X3,and(neg(neg(X2)),or(X,and(neg(X2),neg(neg(X2))))))),
inference(congruence,[status(thm)],[c2059]) ).
cnf(c2061,plain,
and(and(neg(X2),neg(neg(X2))),or(X3,and(neg(neg(X2)),or(X,and(neg(X2),neg(neg(X2))))))) = and(neg(X2),neg(neg(X2))),
inference(substitution,[status(thm)],[c1856]) ).
cnf(c2062,plain,
and(neg(X2),neg(neg(X2))) = and(X,neg(X)),
inference(substitution,[status(thm)],[c2035]) ).
cnf(c2063,plain,
and(and(neg(X3),neg(neg(X3))),or(X4,and(neg(neg(X3)),or(X2,and(neg(X3),neg(neg(X3))))))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c2061,c2062]) ).
cnf(c2064,plain,
and(and(neg(X3),X3),or(X4,and(neg(neg(X3)),or(X2,and(neg(X3),neg(neg(X3))))))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c2060,c2063]) ).
cnf(c2065,plain,
and(and(neg(X3),X3),or(X4,and(neg(neg(X3)),or(X2,and(neg(X3),X3))))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c2057,c2064]) ).
cnf(c2066,plain,
and(and(neg(X3),X3),or(X4,and(X3,or(X2,and(neg(X3),X3))))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c2051,c2065]) ).
cnf(c2067,plain,
and(and(neg(X3),X3),or(X4,and(X3,or(X2,and(X3,neg(X3)))))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c2047,c2066]) ).
cnf(c2068,plain,
and(and(X3,neg(X3)),or(X4,and(X3,or(X2,and(X3,neg(X3)))))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c2041,c2067]) ).
cnf(c2069,plain,
and(and(X5,neg(X5)),or(X4,and(X3,or(X2,and(X3,neg(X3)))))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c2038,c2068]) ).
cnf(c2070,plain,
and(and(X5,neg(X5)),or(X4,and(X3,X2))) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c2022,c2069]) ).
cnf(c2071,plain,
and(and(X4,neg(X4)),or(and(X3,X2),and(X3,X2))) = and(X,neg(X)),
inference(substitution,[status(thm)],[c2070]) ).
cnf(c2072,plain,
and(and(X4,neg(X4)),and(X3,X2)) = and(X,neg(X)),
inference(transitivity,[status(thm)],[c2017,c2071]) ).
cnf(c2073,plain,
and(and(X2,neg(X2)),and(X3,X4)) = and(X,neg(X)),
inference(substitution,[status(thm)],[c2072]) ).
cnf(c2074,plain,
and(X,neg(X)) = and(and(X2,neg(X2)),and(X3,X4)),
inference(symmetry,[status(thm)],[c2073]) ).
cnf(c2075,plain,
or(and(X,neg(X)),and(and(X4,X5),X3)) = or(and(and(X2,neg(X2)),and(X4,X5)),and(and(X4,X5),X3)),
inference(congruence,[status(thm)],[c2074]) ).
cnf(c2076,plain,
and(or(and(X,neg(X)),and(and(X5,X6),X3)),X4) = and(or(and(and(X2,neg(X2)),and(X5,X6)),and(and(X5,X6),X3)),X4),
inference(congruence,[status(thm)],[c2075]) ).
cnf(c2077,plain,
or(and(or(and(X,neg(X)),and(and(X5,X6),X3)),X4),and(and(X5,X6),or(and(and(X5,X6),or(and(X2,neg(X2)),neg(and(X2,neg(X2))))),neg(X3)))) = or(and(or(and(and(X2,neg(X2)),and(X5,X6)),and(and(X5,X6),X3)),X4),and(and(X5,X6),or(and(and(X5,X6),or(and(X2,neg(X2)),neg(and(X2,neg(X2))))),neg(X3)))),
inference(congruence,[status(thm)],[c2076]) ).
cnf(c2078,plain,
or(and(or(and(and(X,neg(X)),and(X4,X5)),and(and(X4,X5),X2)),X3),and(and(X4,X5),or(and(and(X4,X5),or(and(X,neg(X)),neg(and(X,neg(X))))),neg(X2)))) = and(X4,X5),
inference(substitution,[status(thm)],[c1276]) ).
cnf(c2079,plain,
and(X2,X) = and(X,X2),
inference(substitution,[status(thm)],[c934]) ).
cnf(c2080,plain,
and(X,X2) = and(X2,X),
inference(symmetry,[status(thm)],[c2079]) ).
cnf(c2081,plain,
or(and(or(and(and(X,neg(X)),and(X4,X5)),and(and(X4,X5),X2)),X3),and(and(X4,X5),or(and(and(X4,X5),or(and(X,neg(X)),neg(and(X,neg(X))))),neg(X2)))) = and(X5,X4),
inference(transitivity,[status(thm)],[c2078,c2080]) ).
cnf(c2082,plain,
or(and(or(and(X,neg(X)),and(and(X5,X6),X3)),X4),and(and(X5,X6),or(and(and(X5,X6),or(and(X2,neg(X2)),neg(and(X2,neg(X2))))),neg(X3)))) = and(X6,X5),
inference(transitivity,[status(thm)],[c2077,c2081]) ).
cnf(c2083,plain,
or(and(and(and(X4,X5),X2),X3),and(and(X4,X5),or(and(and(X4,X5),or(and(X,neg(X)),neg(and(X,neg(X))))),neg(X2)))) = and(X5,X4),
inference(transitivity,[status(thm)],[c2014,c2082]) ).
cnf(c2084,plain,
or(and(and(and(X4,X5),X2),X3),and(and(X4,X5),or(and(and(X4,X5),neg(and(X,neg(X)))),neg(X2)))) = and(X5,X4),
inference(transitivity,[status(thm)],[c2010,c2083]) ).
cnf(c2085,plain,
or(and(and(and(X4,X5),X2),X3),and(and(X4,X5),or(and(and(X4,X5),or(X,neg(X))),neg(X2)))) = and(X5,X4),
inference(transitivity,[status(thm)],[c2001,c2084]) ).
cnf(c2086,plain,
or(and(and(and(X3,X4),X),X2),and(and(X3,X4),or(and(X3,X4),neg(X)))) = and(X4,X3),
inference(transitivity,[status(thm)],[c1989,c2085]) ).
cnf(c2087,plain,
or(and(and(and(X3,X4),X),X2),and(X3,X4)) = and(X4,X3),
inference(transitivity,[status(thm)],[c1113,c2086]) ).
cnf(c2088,plain,
or(and(X3,X4),and(and(and(X3,X4),X),X2)) = and(X4,X3),
inference(transitivity,[status(thm)],[c998,c2087]) ).
cnf(c2089,plain,
or(and(X3,X4),and(and(and(X4,X3),X),X2)) = and(X4,X3),
inference(transitivity,[status(thm)],[c997,c2088]) ).
cnf(c2090,plain,
or(and(X4,X3),and(and(and(X4,X3),X),X2)) = and(X4,X3),
inference(transitivity,[status(thm)],[c993,c2089]) ).
cnf(c2091,plain,
or(and(X4,X3),and(X2,and(and(X4,X3),X))) = and(X4,X3),
inference(transitivity,[status(thm)],[c991,c2090]) ).
cnf(c2092,plain,
or(and(X4,X3),and(X2,and(X,and(X4,X3)))) = and(X4,X3),
inference(transitivity,[status(thm)],[c989,c2091]) ).
cnf(c2093,plain,
or(and(or(X4,neg(X)),or(X4,and(or(X4,neg(X)),and(neg(X4),X)))),and(X3,and(X2,and(or(X4,neg(X)),or(X4,and(or(X4,neg(X)),and(neg(X4),X))))))) = and(or(X4,neg(X)),or(X4,and(or(X4,neg(X)),and(neg(X4),X)))),
inference(substitution,[status(thm)],[c2092]) ).
cnf(c2094,plain,
or(and(or(X4,neg(X)),or(X4,and(or(X4,neg(X)),and(neg(X4),X)))),and(X3,and(X2,and(or(X4,neg(X)),or(X4,and(or(X4,neg(X)),and(neg(X4),X))))))) = X4,
inference(transitivity,[status(thm)],[c2093,c974]) ).
cnf(c2095,plain,
or(X4,and(X3,and(X2,and(or(X4,neg(X)),or(X4,and(or(X4,neg(X)),and(neg(X4),X))))))) = X4,
inference(transitivity,[status(thm)],[c986,c2094]) ).
cnf(c2096,plain,
or(X3,and(X2,and(X,X3))) = X3,
inference(transitivity,[status(thm)],[c984,c2095]) ).
cnf(c2097,plain,
or(X3,and(X2,and(X3,X))) = X3,
inference(transitivity,[status(thm)],[c980,c2096]) ).
cnf(c2098,plain,
or(or(X3,neg(X2)),and(X,and(or(X3,neg(X2)),or(X3,and(or(X3,neg(X2)),and(neg(X3),X2)))))) = or(X3,neg(X2)),
inference(substitution,[status(thm)],[c2097]) ).
cnf(c2099,plain,
or(or(X3,neg(X2)),and(X,X3)) = or(X3,neg(X2)),
inference(transitivity,[status(thm)],[c977,c2098]) ).
cnf(c2100,plain,
or(or(X3,neg(X2)),and(X3,X)) = or(X3,neg(X2)),
inference(transitivity,[status(thm)],[c967,c2099]) ).
cnf(c2101,plain,
or(or(X3,neg(neg(X2))),and(X3,X)) = or(X3,neg(neg(X2))),
inference(substitution,[status(thm)],[c2100]) ).
cnf(c2102,plain,
or(X2,neg(neg(X))) = or(X2,X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c2103,plain,
or(or(X3,neg(neg(X2))),and(X3,X)) = or(X3,X2),
inference(transitivity,[status(thm)],[c2101,c2102]) ).
cnf(c2104,plain,
or(or(X3,X2),and(X3,X)) = or(X3,X2),
inference(transitivity,[status(thm)],[c965,c2103]) ).
cnf(c2105,plain,
or(or(neg(X3),X4),and(neg(X3),or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(X3,neg(X3))),X)))) = or(neg(X3),X4),
inference(substitution,[status(thm)],[c2104]) ).
cnf(c2106,plain,
or(X2,neg(X)) = or(neg(X),X2),
inference(substitution,[status(thm)],[c913]) ).
cnf(c2107,plain,
or(neg(X),X2) = or(X2,neg(X)),
inference(symmetry,[status(thm)],[c2106]) ).
cnf(c2108,plain,
or(or(neg(X3),X4),and(neg(X3),or(and(neg(X3),X2),and(or(and(neg(X3),X2),and(X3,neg(X3))),X)))) = or(X4,neg(X3)),
inference(transitivity,[status(thm)],[c2105,c2107]) ).
cnf(c2109,plain,
or(or(neg(X2),X3),and(X,neg(X2))) = or(X3,neg(X2)),
inference(transitivity,[status(thm)],[c962,c2108]) ).
cnf(c2110,plain,
or(or(X3,neg(X2)),and(X,neg(X2))) = or(X3,neg(X2)),
inference(transitivity,[status(thm)],[c944,c2109]) ).
cnf(c2111,plain,
or(or(X3,neg(neg(X2))),and(X,neg(neg(X2)))) = or(X3,neg(neg(X2))),
inference(substitution,[status(thm)],[c2110]) ).
cnf(c2112,plain,
or(X2,neg(neg(X))) = or(X2,X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c2113,plain,
or(or(X3,neg(neg(X2))),and(X,neg(neg(X2)))) = or(X3,X2),
inference(transitivity,[status(thm)],[c2111,c2112]) ).
cnf(c2114,plain,
or(or(X3,X2),and(X,neg(neg(X2)))) = or(X3,X2),
inference(transitivity,[status(thm)],[c942,c2113]) ).
cnf(c2115,plain,
or(or(X3,X2),and(X,X2)) = or(X3,X2),
inference(transitivity,[status(thm)],[c939,c2114]) ).
cnf(c2116,plain,
or(or(X3,X2),and(X2,X)) = or(X3,X2),
inference(transitivity,[status(thm)],[c936,c2115]) ).
cnf(c2117,plain,
or(or(X,X3),and(X3,X2)) = or(X,X3),
inference(substitution,[status(thm)],[c2116]) ).
cnf(c2118,plain,
or(X2,X) = or(X,X2),
inference(substitution,[status(thm)],[c913]) ).
cnf(c2119,plain,
or(X,X2) = or(X2,X),
inference(symmetry,[status(thm)],[c2118]) ).
cnf(c2120,plain,
or(or(X,X3),and(X3,X2)) = or(X3,X),
inference(transitivity,[status(thm)],[c2117,c2119]) ).
cnf(c2121,plain,
or(and(X3,X2),or(X,X3)) = or(X3,X),
inference(transitivity,[status(thm)],[c917,c2120]) ).
cnf(c2122,plain,
or(and(or(X2,X4),X),or(X3,or(X2,X4))) = or(or(X2,X4),X3),
inference(substitution,[status(thm)],[c2121]) ).
cnf(c2123,plain,
or(or(X2,X4),X3) = or(and(or(X2,X4),X),or(X3,or(X2,X4))),
inference(symmetry,[status(thm)],[c2122]) ).
cnf(c2124,plain,
or(X2,X) = or(X,X2),
inference(substitution,[status(thm)],[c913]) ).
cnf(c2125,plain,
or(or(X3,X2),or(X3,X)) = or(or(X3,X2),or(X,X3)),
inference(congruence,[status(thm)],[c2124]) ).
cnf(c2126,plain,
or(or(X2,X),X3) = or(X3,or(X2,X)),
inference(substitution,[status(thm)],[c913]) ).
cnf(c2127,plain,
and(or(X3,X2),or(or(X2,X),X3)) = and(or(X3,X2),or(X3,or(X2,X))),
inference(congruence,[status(thm)],[c2126]) ).
cnf(c2128,plain,
and(or(X3,X2),or(X3,or(X2,X))) = and(or(X3,or(X2,X)),or(X3,X2)),
inference(substitution,[status(thm)],[c934]) ).
cnf(c2129,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c2130,plain,
or(X2,X) = or(X2,neg(neg(X))),
inference(congruence,[status(thm)],[c2129]) ).
cnf(c2131,plain,
or(X2,or(X3,X)) = or(X2,or(X3,neg(neg(X)))),
inference(congruence,[status(thm)],[c2130]) ).
cnf(c2132,plain,
and(X3,or(X2,or(X3,X))) = and(X3,or(X2,or(X3,neg(neg(X))))),
inference(congruence,[status(thm)],[c2131]) ).
cnf(c2133,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c2134,plain,
or(X2,or(X3,neg(X))) = or(neg(neg(X2)),or(X3,neg(X))),
inference(congruence,[status(thm)],[c2133]) ).
cnf(c2135,plain,
and(X3,or(X2,or(X3,neg(X)))) = and(X3,or(neg(neg(X2)),or(X3,neg(X)))),
inference(congruence,[status(thm)],[c2134]) ).
cnf(c2136,plain,
or(X2,neg(X)) = or(neg(X),X2),
inference(substitution,[status(thm)],[c913]) ).
cnf(c2137,plain,
or(neg(X2),or(X3,neg(X))) = or(neg(X2),or(neg(X),X3)),
inference(congruence,[status(thm)],[c2136]) ).
cnf(c2138,plain,
and(X3,or(neg(X2),or(X3,neg(X)))) = and(X3,or(neg(X2),or(neg(X),X3))),
inference(congruence,[status(thm)],[c2137]) ).
cnf(c2139,plain,
f(X,neg(X2)) = or(neg(X),X2),
inference(substitution,[status(thm)],[c85]) ).
cnf(c2140,plain,
or(neg(X),X2) = f(X,neg(X2)),
inference(symmetry,[status(thm)],[c2139]) ).
cnf(c2141,plain,
or(neg(X2),or(neg(X),X3)) = or(neg(X2),f(X,neg(X3))),
inference(congruence,[status(thm)],[c2140]) ).
cnf(c2142,plain,
and(X3,or(neg(X2),or(neg(X),X3))) = and(X3,or(neg(X2),f(X,neg(X3)))),
inference(congruence,[status(thm)],[c2141]) ).
cnf(c2143,plain,
neg(and(X,neg(X2))) = f(X,neg(X2)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c2144,plain,
f(X,neg(X2)) = neg(and(X,neg(X2))),
inference(symmetry,[status(thm)],[c2143]) ).
cnf(c2145,plain,
or(neg(X2),f(X,neg(X3))) = or(neg(X2),neg(and(X,neg(X3)))),
inference(congruence,[status(thm)],[c2144]) ).
cnf(c2146,plain,
and(X3,or(neg(X2),f(X,neg(X3)))) = and(X3,or(neg(X2),neg(and(X,neg(X3))))),
inference(congruence,[status(thm)],[c2145]) ).
cnf(c2147,plain,
f(X2,and(X,neg(X3))) = or(neg(X2),neg(and(X,neg(X3)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c2148,plain,
or(neg(X2),neg(and(X,neg(X3)))) = f(X2,and(X,neg(X3))),
inference(symmetry,[status(thm)],[c2147]) ).
cnf(c2149,plain,
and(X3,or(neg(X2),neg(and(X,neg(X3))))) = and(X3,f(X2,and(X,neg(X3)))),
inference(congruence,[status(thm)],[c2148]) ).
cnf(c2150,plain,
neg(and(X2,and(X,neg(X3)))) = f(X2,and(X,neg(X3))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c2151,plain,
f(X2,and(X,neg(X3))) = neg(and(X2,and(X,neg(X3)))),
inference(symmetry,[status(thm)],[c2150]) ).
cnf(c2152,plain,
and(X3,f(X2,and(X,neg(X3)))) = and(X3,neg(and(X2,and(X,neg(X3))))),
inference(congruence,[status(thm)],[c2151]) ).
cnf(c2153,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c2154,plain,
and(X3,neg(and(X2,and(X,neg(X3))))) = and(neg(neg(X3)),neg(and(X2,and(X,neg(X3))))),
inference(congruence,[status(thm)],[c2153]) ).
cnf(c2155,plain,
neg(or(neg(X3),and(X2,and(X,neg(X3))))) = and(neg(neg(X3)),neg(and(X2,and(X,neg(X3))))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c2156,plain,
and(neg(neg(X3)),neg(and(X2,and(X,neg(X3))))) = neg(or(neg(X3),and(X2,and(X,neg(X3))))),
inference(symmetry,[status(thm)],[c2155]) ).
cnf(c2157,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c2158,plain,
or(X2,and(neg(X2),or(X,neg(X)))) = or(neg(neg(X2)),and(neg(X2),or(X,neg(X)))),
inference(congruence,[status(thm)],[c2157]) ).
cnf(c2159,plain,
and(neg(X2),or(X2,and(neg(X2),or(X,neg(X))))) = and(neg(X2),or(neg(neg(X2)),and(neg(X2),or(X,neg(X))))),
inference(congruence,[status(thm)],[c2158]) ).
cnf(c2160,plain,
and(neg(X2),or(neg(neg(X2)),and(neg(X2),or(X,neg(X))))) = neg(X2),
inference(substitution,[status(thm)],[c1282]) ).
cnf(c2161,plain,
and(neg(X2),or(X2,and(neg(X2),or(X,neg(X))))) = neg(X2),
inference(transitivity,[status(thm)],[c2159,c2160]) ).
cnf(c2162,plain,
neg(X2) = and(neg(X2),or(X2,and(neg(X2),or(X,neg(X))))),
inference(symmetry,[status(thm)],[c2161]) ).
cnf(c2163,plain,
and(X2,neg(X3)) = and(X2,and(neg(X3),or(X3,and(neg(X3),or(X,neg(X)))))),
inference(congruence,[status(thm)],[c2162]) ).
cnf(c2164,plain,
and(X3,and(X2,neg(X4))) = and(X3,and(X2,and(neg(X4),or(X4,and(neg(X4),or(X,neg(X))))))),
inference(congruence,[status(thm)],[c2163]) ).
cnf(c2165,plain,
or(neg(X4),and(X3,and(X2,neg(X4)))) = or(neg(X4),and(X3,and(X2,and(neg(X4),or(X4,and(neg(X4),or(X,neg(X)))))))),
inference(congruence,[status(thm)],[c2164]) ).
cnf(c2166,plain,
neg(X2) = and(neg(X2),or(X2,and(neg(X2),or(X,neg(X))))),
inference(symmetry,[status(thm)],[c2161]) ).
cnf(c2167,plain,
or(neg(X4),and(X3,and(X2,and(neg(X4),or(X4,and(neg(X4),or(X,neg(X)))))))) = or(and(neg(X4),or(X4,and(neg(X4),or(X,neg(X))))),and(X3,and(X2,and(neg(X4),or(X4,and(neg(X4),or(X,neg(X)))))))),
inference(congruence,[status(thm)],[c2166]) ).
cnf(c2168,plain,
or(and(neg(X4),or(X4,and(neg(X4),or(X,neg(X))))),and(X3,and(X2,and(neg(X4),or(X4,and(neg(X4),or(X,neg(X)))))))) = and(neg(X4),or(X4,and(neg(X4),or(X,neg(X))))),
inference(substitution,[status(thm)],[c2092]) ).
cnf(c2169,plain,
or(and(neg(X4),or(X4,and(neg(X4),or(X,neg(X))))),and(X3,and(X2,and(neg(X4),or(X4,and(neg(X4),or(X,neg(X)))))))) = neg(X4),
inference(transitivity,[status(thm)],[c2168,c2161]) ).
cnf(c2170,plain,
or(neg(X4),and(X3,and(X2,and(neg(X4),or(X4,and(neg(X4),or(X,neg(X)))))))) = neg(X4),
inference(transitivity,[status(thm)],[c2167,c2169]) ).
cnf(c2171,plain,
or(neg(X3),and(X2,and(X,neg(X3)))) = neg(X3),
inference(transitivity,[status(thm)],[c2165,c2170]) ).
cnf(c2172,plain,
neg(or(neg(X3),and(X2,and(X,neg(X3))))) = neg(neg(X3)),
inference(congruence,[status(thm)],[c2171]) ).
cnf(c2173,plain,
neg(or(neg(X3),and(X2,and(X,neg(X3))))) = X3,
inference(transitivity,[status(thm)],[c2172,c79]) ).
cnf(c2174,plain,
and(neg(neg(X3)),neg(and(X2,and(X,neg(X3))))) = X3,
inference(transitivity,[status(thm)],[c2156,c2173]) ).
cnf(c2175,plain,
and(X3,neg(and(X2,and(X,neg(X3))))) = X3,
inference(transitivity,[status(thm)],[c2154,c2174]) ).
cnf(c2176,plain,
and(X3,f(X2,and(X,neg(X3)))) = X3,
inference(transitivity,[status(thm)],[c2152,c2175]) ).
cnf(c2177,plain,
and(X3,or(neg(X2),neg(and(X,neg(X3))))) = X3,
inference(transitivity,[status(thm)],[c2149,c2176]) ).
cnf(c2178,plain,
and(X3,or(neg(X2),f(X,neg(X3)))) = X3,
inference(transitivity,[status(thm)],[c2146,c2177]) ).
cnf(c2179,plain,
and(X3,or(neg(X2),or(neg(X),X3))) = X3,
inference(transitivity,[status(thm)],[c2142,c2178]) ).
cnf(c2180,plain,
and(X3,or(neg(X2),or(X3,neg(X)))) = X3,
inference(transitivity,[status(thm)],[c2138,c2179]) ).
cnf(c2181,plain,
and(X3,or(neg(neg(X2)),or(X3,neg(X)))) = X3,
inference(substitution,[status(thm)],[c2180]) ).
cnf(c2182,plain,
and(X3,or(X2,or(X3,neg(X)))) = X3,
inference(transitivity,[status(thm)],[c2135,c2181]) ).
cnf(c2183,plain,
and(X3,or(X2,or(X3,neg(neg(X))))) = X3,
inference(substitution,[status(thm)],[c2182]) ).
cnf(c2184,plain,
and(X3,or(X2,or(X3,X))) = X3,
inference(transitivity,[status(thm)],[c2132,c2183]) ).
cnf(c2185,plain,
and(X2,or(X3,or(X2,X))) = X2,
inference(substitution,[status(thm)],[c2184]) ).
cnf(c2186,plain,
X2 = and(X2,or(X3,or(X2,X))),
inference(symmetry,[status(thm)],[c2185]) ).
cnf(c2187,plain,
or(X3,X2) = or(X3,and(X2,or(X3,or(X2,X)))),
inference(congruence,[status(thm)],[c2186]) ).
cnf(c2188,plain,
and(or(X3,or(X2,X)),or(X3,X2)) = and(or(X3,or(X2,X)),or(X3,and(X2,or(X3,or(X2,X))))),
inference(congruence,[status(thm)],[c2187]) ).
cnf(c2189,plain,
and(or(X3,or(X2,X)),or(X3,and(X2,or(X3,or(X2,X))))) = or(X3,and(X2,or(X3,or(X2,X)))),
inference(substitution,[status(thm)],[c1391]) ).
cnf(c2190,plain,
and(X2,or(X3,or(X2,X))) = X2,
inference(substitution,[status(thm)],[c2184]) ).
cnf(c2191,plain,
or(X3,and(X2,or(X3,or(X2,X)))) = or(X3,X2),
inference(congruence,[status(thm)],[c2190]) ).
cnf(c2192,plain,
and(or(X3,or(X2,X)),or(X3,and(X2,or(X3,or(X2,X))))) = or(X3,X2),
inference(transitivity,[status(thm)],[c2189,c2191]) ).
cnf(c2193,plain,
and(or(X3,or(X2,X)),or(X3,X2)) = or(X3,X2),
inference(transitivity,[status(thm)],[c2188,c2192]) ).
cnf(c2194,plain,
and(or(X3,X2),or(X3,or(X2,X))) = or(X3,X2),
inference(transitivity,[status(thm)],[c2128,c2193]) ).
cnf(c2195,plain,
and(or(X3,X2),or(or(X2,X),X3)) = or(X3,X2),
inference(transitivity,[status(thm)],[c2127,c2194]) ).
cnf(c2196,plain,
and(or(X,X3),or(or(X3,X2),X)) = or(X,X3),
inference(substitution,[status(thm)],[c2195]) ).
cnf(c2197,plain,
or(X,X3) = and(or(X,X3),or(or(X3,X2),X)),
inference(symmetry,[status(thm)],[c2196]) ).
cnf(c2198,plain,
or(or(X3,X2),or(X,X3)) = or(or(X3,X2),and(or(X,X3),or(or(X3,X2),X))),
inference(congruence,[status(thm)],[c2197]) ).
cnf(c2199,plain,
and(or(or(X3,X2),X),or(or(X3,X2),and(or(X,X3),or(or(X3,X2),X)))) = or(or(X3,X2),and(or(X,X3),or(or(X3,X2),X))),
inference(substitution,[status(thm)],[c1391]) ).
cnf(c2200,plain,
or(or(X3,X2),and(or(X,X3),or(or(X3,X2),X))) = and(or(or(X3,X2),X),or(or(X3,X2),and(or(X,X3),or(or(X3,X2),X)))),
inference(symmetry,[status(thm)],[c2199]) ).
cnf(c2201,plain,
and(or(X,X3),or(or(X3,X2),X)) = or(X,X3),
inference(substitution,[status(thm)],[c2195]) ).
cnf(c2202,plain,
or(or(X3,X2),and(or(X,X3),or(or(X3,X2),X))) = or(or(X3,X2),or(X,X3)),
inference(congruence,[status(thm)],[c2201]) ).
cnf(c2203,plain,
and(or(or(X3,X2),X),or(or(X3,X2),and(or(X,X3),or(or(X3,X2),X)))) = and(or(or(X3,X2),X),or(or(X3,X2),or(X,X3))),
inference(congruence,[status(thm)],[c2202]) ).
cnf(c2204,plain,
and(or(or(X3,X2),X),or(or(X3,X2),or(X,X3))) = or(or(X3,X2),X),
inference(substitution,[status(thm)],[c2194]) ).
cnf(c2205,plain,
or(X,or(X3,X2)) = or(or(X3,X2),X),
inference(substitution,[status(thm)],[c913]) ).
cnf(c2206,plain,
or(or(X3,X2),X) = or(X,or(X3,X2)),
inference(symmetry,[status(thm)],[c2205]) ).
cnf(c2207,plain,
and(or(or(X3,X2),X),or(or(X3,X2),or(X,X3))) = or(X,or(X3,X2)),
inference(transitivity,[status(thm)],[c2204,c2206]) ).
cnf(c2208,plain,
and(or(or(X3,X2),X),or(or(X3,X2),and(or(X,X3),or(or(X3,X2),X)))) = or(X,or(X3,X2)),
inference(transitivity,[status(thm)],[c2203,c2207]) ).
cnf(c2209,plain,
or(or(X3,X2),and(or(X,X3),or(or(X3,X2),X))) = or(X,or(X3,X2)),
inference(transitivity,[status(thm)],[c2200,c2208]) ).
cnf(c2210,plain,
or(or(X3,X2),or(X,X3)) = or(X,or(X3,X2)),
inference(transitivity,[status(thm)],[c2198,c2209]) ).
cnf(c2211,plain,
or(or(X3,X2),or(X3,X)) = or(X,or(X3,X2)),
inference(transitivity,[status(thm)],[c2125,c2210]) ).
cnf(c2212,plain,
or(or(X,X3),or(X,X2)) = or(X2,or(X,X3)),
inference(substitution,[status(thm)],[c2211]) ).
cnf(c2213,plain,
or(X2,or(X,X3)) = or(or(X,X3),or(X,X2)),
inference(symmetry,[status(thm)],[c2212]) ).
cnf(c2214,plain,
or(and(or(X2,X4),X),or(X3,or(X2,X4))) = or(and(or(X2,X4),X),or(or(X2,X4),or(X2,X3))),
inference(congruence,[status(thm)],[c2213]) ).
cnf(c2215,plain,
or(and(X3,X2),or(X3,X)) = or(or(X3,X),and(X3,X2)),
inference(substitution,[status(thm)],[c913]) ).
cnf(c2216,plain,
or(or(X3,X),and(X3,X2)) = or(X3,X),
inference(substitution,[status(thm)],[c2104]) ).
cnf(c2217,plain,
or(and(X3,X2),or(X3,X)) = or(X3,X),
inference(transitivity,[status(thm)],[c2215,c2216]) ).
cnf(c2218,plain,
or(and(or(X2,X4),X),or(or(X2,X4),or(X2,X3))) = or(or(X2,X4),or(X2,X3)),
inference(substitution,[status(thm)],[c2217]) ).
cnf(c2219,plain,
or(or(X3,X2),or(X3,X)) = or(or(X3,X),or(X3,X2)),
inference(substitution,[status(thm)],[c913]) ).
cnf(c2220,plain,
or(or(X3,X),or(X3,X2)) = or(X2,or(X3,X)),
inference(substitution,[status(thm)],[c2211]) ).
cnf(c2221,plain,
or(or(X3,X2),or(X3,X)) = or(X2,or(X3,X)),
inference(transitivity,[status(thm)],[c2219,c2220]) ).
cnf(c2222,plain,
or(or(X,X3),or(X,X2)) = or(X3,or(X,X2)),
inference(substitution,[status(thm)],[c2221]) ).
cnf(c2223,plain,
or(X2,X) = or(X,X2),
inference(substitution,[status(thm)],[c913]) ).
cnf(c2224,plain,
or(X,X2) = or(X2,X),
inference(symmetry,[status(thm)],[c2223]) ).
cnf(c2225,plain,
or(X3,or(X,X2)) = or(X3,or(X2,X)),
inference(congruence,[status(thm)],[c2224]) ).
cnf(c2226,plain,
or(or(X,X3),or(X,X2)) = or(X3,or(X2,X)),
inference(transitivity,[status(thm)],[c2222,c2225]) ).
cnf(c2227,plain,
or(and(or(X2,X4),X),or(or(X2,X4),or(X2,X3))) = or(X4,or(X3,X2)),
inference(transitivity,[status(thm)],[c2218,c2226]) ).
cnf(c2228,plain,
or(and(or(X2,X4),X),or(X3,or(X2,X4))) = or(X4,or(X3,X2)),
inference(transitivity,[status(thm)],[c2214,c2227]) ).
cnf(c2229,plain,
or(or(X,X3),X2) = or(X3,or(X2,X)),
inference(transitivity,[status(thm)],[c2123,c2228]) ).
cnf(c2230,plain,
or(X2,or(X,X3)) = or(X3,or(X2,X)),
inference(transitivity,[status(thm)],[c916,c2229]) ).
cnf(c2231,plain,
or(X2,or(X3,X)) = or(X3,or(X2,X)),
inference(transitivity,[status(thm)],[c915,c2230]) ).
cnf(c2232,plain,
or(neg(x0),or(neg(x1),neg(x2))) = or(neg(x1),or(neg(x0),neg(x2))),
inference(substitution,[status(thm)],[c2231]) ).
cnf(c2233,plain,
f(x1,neg(or(neg(x0),neg(x2)))) = or(neg(x1),or(neg(x0),neg(x2))),
inference(substitution,[status(thm)],[c85]) ).
cnf(c2234,plain,
or(neg(x1),or(neg(x0),neg(x2))) = f(x1,neg(or(neg(x0),neg(x2)))),
inference(symmetry,[status(thm)],[c2233]) ).
cnf(c2235,plain,
f(x0,x2) = or(neg(x0),neg(x2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c2236,plain,
or(neg(x0),neg(x2)) = f(x0,x2),
inference(symmetry,[status(thm)],[c2235]) ).
cnf(c2237,plain,
neg(or(neg(x0),neg(x2))) = neg(f(x0,x2)),
inference(congruence,[status(thm)],[c2236]) ).
cnf(c2238,plain,
f(x1,neg(or(neg(x0),neg(x2)))) = f(x1,neg(f(x0,x2))),
inference(congruence,[status(thm)],[c2237]) ).
cnf(c2239,plain,
neg(f(x0,x2)) = f(f(x0,x2),f(x0,x2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c2240,plain,
f(x1,neg(f(x0,x2))) = f(x1,f(f(x0,x2),f(x0,x2))),
inference(congruence,[status(thm)],[c2239]) ).
cnf(c2241,plain,
f(x1,neg(or(neg(x0),neg(x2)))) = f(x1,f(f(x0,x2),f(x0,x2))),
inference(transitivity,[status(thm)],[c2238,c2240]) ).
cnf(c2242,plain,
or(neg(x1),or(neg(x0),neg(x2))) = f(x1,f(f(x0,x2),f(x0,x2))),
inference(transitivity,[status(thm)],[c2234,c2241]) ).
cnf(c2243,plain,
or(neg(x0),or(neg(x1),neg(x2))) = f(x1,f(f(x0,x2),f(x0,x2))),
inference(transitivity,[status(thm)],[c2232,c2242]) ).
cnf(c2244,plain,
f(x0,neg(or(neg(x1),neg(x2)))) = f(x1,f(f(x0,x2),f(x0,x2))),
inference(transitivity,[status(thm)],[c91,c2243]) ).
cnf(c2245,plain,
f(x0,neg(f(x1,x2))) = f(x1,f(f(x0,x2),f(x0,x2))),
inference(transitivity,[status(thm)],[c90,c2244]) ).
cnf(c2246,plain,
f(x0,f(f(x1,x2),f(x1,x2))) = f(x1,f(f(x0,x2),f(x0,x2))),
inference(transitivity,[status(thm)],[c5,c2245]) ).
cnf(c2247,plain,
$false,
inference(resolution,[status(thm)],[c1,c2246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT393-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 15:14:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.70/2.50 Command-line arguments: --no-flatten-goal
% 15.70/2.50
% 15.70/2.50 % SZS status Unsatisfiable
% 15.70/2.50
% 18.71/2.82 % SZS output start CNFRefutation
% See solution above
% 30.73/4.35
% 30.73/4.35 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------